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.
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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.