On certain groups with Chernikov group of automorphisms

O.O. Pypka (Oles Honchar Dnipropetrovsk National University)


We obtained automorphic analogue of Schur’s theorem for the case when an arbitrary subgroup A of automorphism group Aut(G) of a group G and the factor-group of a group G modulo A-center are Chernikov groups.


A-center; A-commutator subgroup; Chernikov group


Schur I. "Uber die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen", Journal fur die Reine und Angewandte Mathematik, 1904; 127: pp. 20-50. (in German)

Karpilovsky G. The Schur multiplier, Clarendon Press, Oxford, 1987; 302 p.

Baer R. "Endlichkeitskriterien fur Kommutatorgruppen", Mathematische Annalen, 1952; 124(1): pp. 161-177. (in German) doi:10.1007/BF01343558

Wiegold J. "Multiplicators and groups with finite central factor-groups", Mathematische Zeitschrift, 1965; 89(4): pp. 345-347. doi:10.1007/BF01112166

Franciosi S., de Giovanni F., Kurdachenko L.A. "The Schur property and groups with uniform conjugate classes", Journal of Algebra, 1995; 174(3): pp. 823-847. doi:10.1006/jabr.1995.1155

Hegarty P. "The absolute centre of a group", Journal of Algebra, 1994; 169(3): pp. 929-935. doi:10.1006/jabr.1994.1318

Dixon M.R., Kurdachenko L.A., Pypka A.A. "On Some Variants of Theorems of Schur and Baer", Milan Journal of Mathematics (online version), 2014; 82: pp. 233-241. doi:10.1007/s00032-014-0215-9

Polovicky Ya.D. "Groups with extremal classes of conjugate elements", Siberian Mathematical Journal, 1964; 5(4): pp. 891-895. (in Russian)

Kurdachenko L.A., Otal J. "The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group", Central European Journal of Mathematics, 2013; 11(10): pp. 1732-1741. doi:10.2478/s11533-013-0284-y

DOI: https://doi.org/10.15421/241409



  • There are currently no refbacks.

Copyright (c) 2014 O.O. Pypka

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Registered in


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991