Z. Arad, W. Herfort:

"Classification of Finite Groups with a CC-Subgroup";

Communications in Algebra,32(2004), 6; 2087 - 2098.

A proper subgroup M of a group G is called a CC-subgroup

of G if the centralizer C_G(m) of every m\in M^{\#} is contained in M. Making use of work of Suzuki, Feit, Thompson, Arad, Chillag, Herzog, and many others, the authors provide a complete classification of all groups with such a subgroup M.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC04969716

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