Groups in which every non-cyclic subgroup contains its centralizer

Published 18 May 2013 in math.GR | (1305.4236v1)

Abstract: We study groups having the property that every non-cyclic subgroup contains its centralizer. The structure of nilpotent and supersolvable groups in this class is described. We also classify finite $p$-groups and finite simple groups with the above defined property.

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