Classification of Finite Groups with a CC-Subgroup

Abstract

A proper subgroup M of a group G is called a CC-subgroup of G if the centralizer C _G (m) of every m ∈ M ^# = M ∖ {1} is contained in M. In this paper we classify all finite groups containing a CC-subgroup, extending work of many authors.

Key Words:

• CC-subgroups
• Prime graph

Mathematics Subject Classification:

• 20D25
• 20D40

Acknowledgments

The authors would like to thank the referee for valuable suggestions leading to corrections and significant reductions of some of the proofs as well as a much clearer restructuring of the presentation of the results.

The second author would like to express grateful thanks for the hospitality of the Bar-Ilan University, the Netanya Academic College and the Tel-Aviv University in February 2000.

Notes

^#Communicated by A. Turull.