We extend to soluble FC∗ -groups, the class of generalised FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes , Serdica Math. J. 28(3) (2002), 241 254], the characterisation of finite soluble T-groups obtained recently in [G. Kaplan, On T-groups, supersolvable groups and maximal subgroups , Arch. Math. 96 (2011), 19 25]. ; The first author has been supported by the research grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain and FEDER, European Union. ; Esteban Romero, R.; Vincenzi, G. (2016). On generalised FC-groups in which normality is a transitive relation. Journal of the Australian Mathematical Society. 100(2):192-198. https://doi.org/10.1017/S1446788715000397 ; S ; 192 ; 198 ; 100 ; 2
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of Itˆo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. The following result of Gasch¨utz and Itˆo (see [5, Kapitel IV, Satz 5.7; 9]) gives interesting properties of groups with all minimal subgroups normal. ; The first author has been supported by the research grant MTM2014-54707-C03-1-P from the Ministerio de Economia y Competitividad, Spain and FEDER, European Union. The research of the second author has been done during some visits to the Departament de Matematica Aplicada and the Institut de Matematica Pura i Aplicada of the Universitat Politecnica de Valencia and the Departament d' Algebra of the Universitat de Valencia. She expresses her gratitude to these institutions for the use of their facilities and, especially to the first university for the financial support of some of the visits. ; Esteban Romero, R.; Liriano, O. (2016). Finite groups with all minimal subgroups solitary. Journal of Algebra and Its Applications. 15(8):1650140-1-1650140-9. https://doi.org/10.1142/S0219498816501401 ; S ; 1650140-1 ; 1650140-9 ; 15 ; 8
2945 2952 44 7 ; S ; This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 01 Jun 2016, available online: http://www.tandfonline.com/10.1080/00927872.2015.1065855. We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N . We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups. The first author has been supported by the research grants MTM2010-19038-C03-01 from Ministerio de Ciencia e Innovacion, Spain, MTM2014-54707-C3-1-P from Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The research of the second author has been done during some visits to the Departament de Matematica Aplicada and the Institut Universitari de Matematica Pura i Aplicada of the Universitat Politecnica de Valencia and the Departament d'Algebra of the Universitat de Valencia. She wants to express her gratitude to these institutions for the use of their facilities and, especially to the first university for the financial support of some of the visits. Esteban Romero, R.; Liriano, O. (2016). A note on solitary subgroups of finite groups. Communications in Algebra. 44(7):2945-2952. https://doi.org/10.1080/00927872.2015.1065855
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 01 Jun 2016, available online: http://www.tandfonline.com/10.1080/00927872.2015.1065855. ; We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N . We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups. ; The first author has been supported by the research grants MTM2010-19038-C03-01 from Ministerio de Ciencia e Innovacion, Spain, MTM2014-54707-C3-1-P from Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The research of the second author has been done during some visits to the Departament de Matematica Aplicada and the Institut Universitari de Matematica Pura i Aplicada of the Universitat Politecnica de Valencia and the Departament d'Algebra of the Universitat de Valencia. She wants to express her gratitude to these institutions for the use of their facilities and, especially to the first university for the financial support of some of the visits. ; Esteban Romero, R.; Liriano, O. (2016). A note on solitary subgroups of finite groups. Communications in Algebra. 44(7):2945-2952. https://doi.org/10.1080/00927872.2015.1065855 ; S ; 2945 ; 2952 ; 44 ; 7
The research of this paper has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union, by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union, and by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain. The first author is supported by the predoctoral grant 201606890006 from the China Scholarship Council. The second author is supported by the grant 11401597 from the National Science Foundation of Chin ; Meng, H.; Ballester-Bolinches, A.; Esteban Romero, R. (2019). On large orbits of supersoluble subgroups of linear groups. Journal of the London Mathematical Society. 101(2):490-504. https://doi.org/10.1112/jlms.12266 ; S ; 490 ; 504 ; 101 ; 2 ; Doerk, K., & Hawkes, T. O. (1992). Finite Soluble Groups. doi:10.1515/9783110870138 ; Dolfi, S. (2008). Large orbits in coprime actions of solvable groups. Transactions of the American Mathematical Society, 360(01), 135-153. doi:10.1090/s0002-9947-07-04155-4 ; Dolfi, S., & Jabara, E. (2007). Large character degrees of solvable groups with abelian Sylow 2-subgroups. Journal of Algebra, 313(2), 687-694. doi:10.1016/j.jalgebra.2006.12.004 ; Espuelas, A. (1991). Large character degrees of groups of odd order. Illinois Journal of Mathematics, 35(3). doi:10.1215/ijm/1255987794 ; The GAP group 'GAP – groups algorithms and programming version 4.9.1' 2018 http://www.gap‐system.org. ; Halasi, Z., & Maróti, A. (2015). The minimal base size for a 𝑝-solvable linear group. Proceedings of the American Mathematical Society, 144(8), 3231-3242. doi:10.1090/proc/12974 ; Huppert, B. (1967). Endliche Gruppen I. Grundlehren der mathematischen Wissenschaften. doi:10.1007/978-3-642-64981-3 ; Keller, T. M., & Yang, Y. (2015). Abelian quotients and orbit sizes of solvable linear groups. Israel Journal of Mathematics, 211(1), 23-44. doi:10.1007/s11856-015-1259-4 ; Manz, ...
[EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2 (5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201 206, 2012). ; The first and second author are supported by the Grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The first author is supported by the National Natural Science Foundation of China (11271085) and a Project of Natural Science Foundation of Guangdong Province (2015A030313791). The third author is supported by the National Natural Science Foundation of China (11461007), and the Guangxi Natural Science Foundation Program (2016GXNSFAA380156). This research has been done during a visit of the third author to the Departament de Matematiques of the Universitat de Valencia. He expresses his gratitude to this institution. We thank the anonymous referee for his/her comments that have helped us to improve the presentation of the paper. ; Ballester-Bolinches, A.; Esteban Romero, R.; Lu, J. (2017). On finite groups with many supersoluble subgroups. Archiv der Mathematik. 109(1):3-8. https://doi.org/10.1007/s00013-017-1041-4 ; S ; 3 ; 8 ; 109 ; 1 ; J. Bray, D. Holt, and C. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups, London Math. Soc. Lect. Note Ser. Cambridge Univ. Press, Cambridge, UK, 2013. ; L. E. Dickson, Linear groups: With an exposition of the Galois field theory, Dover Publications Inc., New York, 1958. ; K. Doerk and T. Hawkes, Finite Soluble Groups, volume 4 of De Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin, New York, 1992. ; The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.8.6, November 2016. http://www.gap-system.org . ...
[EN] Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang¿Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang¿Baxter equation have been extensively investigated recently. The main aim of this paper is to introduce and study two finite brace theoretical properties associated with nilpotency, and to analyse their impact on the finite solutions of the Yang¿Baxter equation. ; This work was supported by the research grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spanish Government, and FEDER, European Union, and PROMETEO/2017/057 from Generalitat (Valencian Community, Spain). The first author was supported by grant number 201606890006 of the China Scholarship Council. ; Meng, H.; Ballester Bolinches, A.; Esteban Romero, R. (2019). Left braces and the quantum Yang-Baxter equation. Proceedings of the Edinburgh Mathematical Society. 62(2):595-608. https://doi.org/10.1017/S0013091518000664 ; S ; 595 ; 608 ; 62 ; 2 ; Yang, C. N. (1967). Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction. Physical Review Letters, 19(23), 1312-1315. doi:10.1103/physrevlett.19.1312 ; Smoktunowicz, A. (2018). On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation. Transactions of the American Mathematical Society, 370(9), 6535-6564. doi:10.1090/tran/7179 ; Etingof, P., Schedler, T., & Soloviev, A. (1999). Set-theoretical solutions to the quantum Yang-Baxter equation. Duke Mathematical Journal, 100(2), 169-209. doi:10.1215/s0012-7094-99-10007-x ; Cedó, F., Jespers, E., & Okniński, J. (2014). Braces and the Yang–Baxter Equation. Communications in Mathematical Physics, 327(1), 101-116. doi:10.1007/s00220-014-1935-y ; Cedó, F., Gateva-Ivanova, T., & Smoktunowicz, A. (2017). On the Yang–Baxter equation and left nilpotent left braces. Journal of Pure and Applied Algebra, 221(4), 751-756. ...
The final publication is available at Springer via http://dx.doi.org/10.1007/s00013-016-0901-7 ; In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to . We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing such that , if is S-semipermutable in for all normal subgroups H of P with , then either G is p-supersoluble or else . This extends the main result of Guo and Isaacs in (Arch. Math. 105:215-222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups. ; The first and the second authors have been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The first author has been also supported by NSC of China (No. 11271085) and a project of Natural Science Foundation of Guangdong Province (No. 2015A030313791). The third author was supported by NSF of China (No. 11201082), Cultivation Program for Outstanding Young College Teachers (Yq2013061) and Project (2013B051000075) of Guangdong Province, Pei Ying Yu Cai Project of GDUT. The third author also thanks the China Scholarship Council and the Departament d'Algebra of the Universitat de Valencia for its hospitality. ; Ballester-Bolinches, A.; Esteban Romero, R.; Qiao, S. (2016). A note on a result of Guo and Isaacs about p-supersolubility of finite groups. Archiv der Mathematik. 106(6):501-506. https://doi.org/10.1007/s00013-016-0901-7 ; S ; 501 ; 506 ; 106 ; 6 ; Ballester-Bolinches A., Esteban-Romero R., Asaad M.: Products of finite groups, volume 53 of de Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin (2010) ; Guo Y., Isaacs I. M.: Conditions on p-subgroups implying p-nilpotence or p-supersolvability. Arch. Math. 105, 215–222 (2015) ; B. Huppert, Endliche ...
The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at every step are ignored. However, we can also take into account the different decisions which can be made at every state, that is, the branches that can be taken, and these decisions might change the possible future behaviour. In this case, the behaviour of the automata can be described with the help of the concept of bisimilarity. This is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras. Contrarily to what happens with deterministic automata, it is not possible to describe the behaviour up to bisimilarity of states of a non-deterministic automaton by considering just the languages associated to them. In this paper we present a description of a final object for the category of non-deterministic automata, regarded as labelled transition systems, with the help of some structures defined in terms of languages. As a consequence, we obtain a characterisation of bisimilarity of states of automata in terms of languages and a method to minimise non-deterministic automata with respect to bisimilarity of states. This confirms that languages can be considered as the natural objects to describe the behaviour of automata. (C) 2014 Elsevier B.V. All rights reserved. ; This work has been supported by the grant MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovacion (Spanish Government). The first author has been supported by a research project from the National Natural Science Foundation of China (NSFC, No. 11271085). The second author has been supported by the predoctoral grant AP2010-2764 from the Ministerio de Educacion (Spanish Government). We also thank Jean-Eric Pin and Jan Rutten for their helpful comments. Finally, we are indebted to the anonymous referees for their careful reading of the paper and for bringing to our ...
This paper has been published in Science China Mathematics, 55(5):961-966 (2012). Copyright 2012 by Science China Press and Springer-Verlag. The final publication is available at www.springerlink.com. http://link.springer.com/article/10.1007/s11425-011-4356-9 http://dx.doi.org/10.1007/s11425-011-4356-9 ; A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series. The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors. However there are still some open questions which deserve an answer. The purpose of the present paper is to give a complete answer to one of these questions. ; This work was supported by MEC of Spain, FEDER of European Union (Grant No. MTM-2007-68010-C03-02), MICINN of Spain (Grant No. MTM-2010-19938-C03-01), National Natural Science Foundation of China (Grant No. 11171353/A010201) and Natural Science Fund of Guangdong (Grant No. S2011010004447). Part of this research was carried out during a visit of the third author to the Departament d'Algebra, Universitat de Valencia, Burjassot, Valencia, Spain, and the Institut Universitari de Matematica Pura i Aplicada, Universitat Politecnica de Valencia, Valencia, Spain, between September, 2009 and August, 2010. He is grateful to both institutions for their warm hospitality and, in particular, to the Universitat Politecnica de Valencia for the financial support given via its Programme of Support to Research and Development 2010. ; http://link.springer.com/article/10.1007/s11425-011-4356-9 ; Ballester Bolinches, A.; Esteban Romero, R.; Li, Y. (2012). A question on partial CAP-subgroups of finite groups. Science China Mathematics. 5(55). doi:10.1007/s11425-011-4356-9 ; S ; 5 ; 55 ; Ballester-Bolinches A, Ezquerro L M. Classes of Finite Groups. In: Mathematics and its Applications, vol. 584. New York: Springer, 2006 ; Ballester-Bolinches A, Ezquerro L M, Skiba A N. Local ...
This paper has been published in Bulletin of the Australian Mathematical Society, 86(1):22-28 (2012). Copyright 2012 by Australian Mathematical Publishing Association Inc and Cambridge University Press Journals. The final publication is available at http://journals.cambridge.org/abstract_S0004972711003418 ; In this paper, solubility of groups factorised as a product of two subgroups which are connected by certain permutability properties is studied. ; The research of the second and the third authors has been supported by the grant MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovacion (Spanish government). ; http://dx.doi.org/10.1017/S0004972711003418 ; Asaad, M.; Ballester Bolinches, A.; Esteban Romero, R. (2012). Some solubility criteria in factorised groups. Bulletin of the Australian Mathematical Society. (86). doi:10.1017/S0004972711003418 ; S ; 86 ; Maier, R. (1989). Zur Vertauschbarkeit und Subnormalit�t von Untergruppen. Archiv der Mathematik, 53(2), 110-120. doi:10.1007/bf01198559 ; Huppert, B. (1967). Endliche Gruppen I. Grundlehren der mathematischen Wissenschaften. doi:10.1007/978-3-642-64981-3 ; Doerk, K., & Hawkes, T. O. (1992). Finite Soluble Groups. doi:10.1515/9783110870138 ; Deskins, W. E. (1959). On maximal subgroups. Finite Groups, 100-104. doi:10.1090/pspum/001/0125157 ; Ballester-Bolinches, A., Esteban-Romero, R., & Asaad, M. (2010). Products of Finite Groups. de Gruyter Expositions in Mathematics. doi:10.1515/9783110220612 ; Ballester-Bolinches, A., Guo, X., & Pedraza-Aguilera, M. C. (2000). A note on m-permutable products of finite groups. Journal of Group Theory, 3(4). doi:10.1515/jgth.2000.030 ; Ballester-Bolinches, A., Cossey, J., & Pedraza-Aguilera, M. C. (2001). ON PRODUCTS OF FINITE SUPERSOLUBLE GROUPS. Communications in Algebra, 29(7), 3145-3152. doi:10.1081/agb-5013 ; Ezquerro, L. M., & Soler-Escrivà, X. (2003). On MutuallyM-Permutable Products of Finite Groups. Communications in Algebra, 31(4), 1949-1960. doi:10.1081/agb-120018515
5 55 ; S Huppert B. Endliche Gruppen I. In: Grund Math Wiss, vol. 134. Berlin-Heidelberg-New York: Springer-Verlag, 1967 Huppert B, Blackburn N. Finite Groups III. In: Grund Math Wiss, vol. 243. Berlin: Springer-Verlag, 1982 ; This paper has been published in Science China Mathematics, 55(5):961-966 (2012). Copyright 2012 by Science China Press and Springer-Verlag. The final publication is available at www.springerlink.com. http://link.springer.com/article/10.1007/s11425-011-4356-9 http://dx.doi.org/10.1007/s11425-011-4356-9 A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series. The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors. However there are still some open questions which deserve an answer. The purpose of the present paper is to give a complete answer to one of these questions. This work was supported by MEC of Spain, FEDER of European Union (Grant No. MTM-2007-68010-C03-02), MICINN of Spain (Grant No. MTM-2010-19938-C03-01), National Natural Science Foundation of China (Grant No. 11171353/A010201) and Natural Science Fund of Guangdong (Grant No. S2011010004447). Part of this research was carried out during a visit of the third author to the Departament d'Algebra, Universitat de Valencia, Burjassot, Valencia, Spain, and the Institut Universitari de Matematica Pura i Aplicada, Universitat Politecnica de Valencia, Valencia, Spain, between September, 2009 and August, 2010. He is grateful to both institutions for their warm hospitality and, in particular, to the Universitat Politecnica de Valencia for the financial support given via its Programme of Support to Research and Development 2010. http://link.springer.com/article/10.1007/s11425-011-4356-9 Ballester Bolinches, A.; Esteban Romero, R.; Li, Y. (2012). A question on partial CAP-subgroups of finite groups. Science China Mathematics. 5(55). ...
This paper has been published in Journal of Group Theory, 13(1):143-149 (2010). Copyright 2010 by Walter de Gruyter. The final publication is available at www.degruyter.com. http://dx.doi.org/10.1515/jgt.2009.038 http://www.degruyter.com/view/j/jgth.2010.13.issue-1/jgt.2009.038/jgt.2009.038.xml ; [EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively. ; This research was supported by the grants MTM2004-08219C02-02 and MTM2007-68010-C03-02 from MEC (Spanish Government) and FEDER (European Union) and GV/2007/243 from Generalitat (Valencian Community). ; http://dx.doi.org/10.1515/jgt.2009.038 ; Ballester Bolinches, A.; Esteban Romero, R.; Li, Y. (2010). On self-normalizing subgroups of finite groups. Journal of Group Theory. 1(13). https://doi.org/10.1515/jgt.2009.038 ; 1 ; 13 ; Agrawal, R. K. (1975). Finite Groups whose Subnormal Subgroups Permute with all Sylow Subgroups. Proceedings of the American Mathematical Society, 47(1), 77. doi:10.2307/2040211 ; Alejandre, M. J., Ballester-Bolinches, A., & Pedraza-Aguilera, M. . (2001). Finite Soluble Groups with Permutable Subnormal Subgroups. Journal of Algebra, 240(2), 705-722. doi:10.1006/jabr.2001.8732 ; Ballester-Bolinches, A., & Esteban-Romero, R. (2001). Sylow permutable subnormal subgroups of finite groups II. Bulletin of the Australian Mathematical Society, 64(3), 479-486. doi:10.1017/s0004972700019948 ; Ballester-Bolinches, A., & Esteban-Romero, R. (2002). Sylow Permutable Subnormal Subgroups of Finite Groups. Journal of Algebra, 251(2), 727-738. doi:10.1006/jabr.2001.9138 ; Beidleman, J. C., Brewster, B., & Robinson, D. J. S. (1999). Criteria for Permutability to Be Transitive in Finite Groups. Journal of Algebra, 222(2), 400-412. doi:10.1006/jabr.1998.7964 ; Beidleman, J. C., Heineken, H., & Ragland, M. F. ...
[EN] This paper has been published in Journal of Group Theory, 12(6):961-963 (2009). Copyright 2009 by Walter de Gruyter. The final publication is available at www.degruyter.com. http://dx.doi.org/10.1515/JGT.2009.026 http://www.degruyter.com/view/j/jgth.2009.12.issue-6/jgt.2009.026/jgt.2009.026.xml ; This is a corrigendum to "A Note on Finite PST-Groups" (J. Group Theory 10 (2007), 205-210). ; This research has been supported by the grants MTM2004-08219-C02-02 and MTM2007-68010-C03-02 from MEC (Spanish Government) and FEDER (European Union) and GV/2007/243 from Generalitat (València) ; http://dx.doi.org/10.1515/JGT.2009.026 ; Ballester Bolinches, A.; Esteban Romero, R.; Ragland, MF. (2009). Corrigendum: A note on finite PST-groups [J. Group Theory 10 (2007), 205-210]. Journal of Group Theory. 6(12). https://doi.org/10.1515/JGT.2009.026 ; 6 ; 12
[EN] A group G is said to be an involutive Yang¿Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, nondegenerate set-theoretic solution of the Yang-Baxter equation. We give new sufficient conditions for a group that can be factorised as a product of two IYB-groups to be an IYB-group. Some earlier results are direct consequences of our main theorem. ; The research of this paper was supported by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union, and by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain. The first author was supported by the predoctoral grant 201606890006 from the China Scholarship Council. The fourth author was supported by a predoctoral grant from the "Atraccio del talent" Programme from the Universitat de Valencia. ; Meng, H.; Ballester-Bolinches, A.; Esteban Romero, R.; Fuster-Corral, N. (2021). On finite involutive Yang-Baxter groups. Proceedings of the American Mathematical Society. 149(2):793-804. https://doi.org/10.1090/proc/15283 ; S ; 793 ; 804 ; 149 ; 2
