Primitive subgroups and PST-groups

Authors

  • A. Ballester-Bolinches
  • J. C. Beidleman University of Kentucky
  • R. Esteban-Romeo

Abstract

All groups considered in this paper are finite. A subgroup \(H\) of group \(G\) is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of \(G\) containing \(H\) as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. \(28\)(1) (2013), 55–62] proved that every primitive subgroup of \(G\) has index a power of a prime if and only if G/(frattini-subgroup) is a solvable PST-group. Let \(X\) denote the class of groups \(G\) all of whose primitive sub-groups have prime power index. It is established here that a group \(G\) is a solvable PST-group if and only if every subgroup of \(G\) is an \(X\)-group. DOI: 10.1017/S0004972713000592

Author Biography

J. C. Beidleman, University of Kentucky

Full Professor, Mathematics Department

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles
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