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7 pags., 3 figs., 1 tab. ; States in the N = 35 and 37 isotopes 55,57Ca have been populated by direct proton-induced nucleon removal reactions from 56,58Sc and 56Ca beams at the RIBF. In addition, the (p, 2p) quasi-free single- proton removal reaction from 56Ca was studied. Excited states in 55K, 55Ca, and 57Ca were established for the first time via in-beam γ -ray spectroscopy. Results for the proton and neutron removal reactions from 56Ca to states in 55K and 55Ca for the level energies, excited state lifetimes, and exclusive cross sections agree well with state-of-the-art theoretical calculations using different approaches. The observation of a short-lived state in 57Ca suggests a transition in the calcium isotopic chain from single-particle dominated states at N = 35 to collective excitations at N = 37. ; We would like to thank the RIKEN accelerator and BigRIPS teams for providing the high intensity beams. T.K. acknowledges support by RIKEN Junior Research Associate Program. K.W. acknowledges support from the Spanish Ministerio de Ciencia, Innovación y Universidades RYC-2017-22007. RIUMF receives funding via a contribution through the National Research Council of Canada. J.D.H is further supported by NSERC under grants SAPIN-2018-00027 and RGPAS-2018-522453. VS-IMSRG computations were performed with an allocation of computing resources on Cedar at WestGrid and Compute Canada, and on the Oak Cluster at TRIUMF managed by the University of British Columbia department of Advanced Research Computing (ARC). N.S. and Y.U. acknowledge valuable support by "Priority Issue on post-K computer" and KAKENHI grant 20K03981 and 17K05433. C.B. was supported by the UK Science and Technology Facilities Council (STFC) through grants No. ST/L005816/1 and No. ST/V001108/1. SCGF calculations were per- formed by using HPC resources from GENCI-TGCC, France (Contract No. A009057392) and at the DiRAC DiAL system at the University of Leicester, UK, (funded by the UK BEIS via STFC Capital Grants No. ST/K000373/1 and No. ST/R002363/1 and STFC DiRAC Operations Grant No. ST/R001014/1). I.M. was supported by the RIKEN IPA program, F.B. by the RIKEN Special Postdoctoral Researche Program. D.S. acknowledges support from the European Regional Development Fund contract No. GINOP-2.3.3-15-2016-00034 and the National Research, Development and Innovation Fund of Hungary via Project No. K128947. K. I. H., D. K., and S. Y. P. acknowledge the support from the IBS grant funded by the Korea government (No. IBS-R031-D1). The work was further supported by JSPS KAKENHI Grant Nos. JP16H02179, JP18H05404, JP19H00679, and JP21H01114 and the Deutsche Forschungsgemeinschaft (DFG) under Grant No. BL 1513/1-1 ; Peer reviewed