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arXiv:1205.0643 [math.GR]AbstractReferencesReviewsResources

On solubility of groups with finitely many centralizers

Mohammad Zarrin

Published 2012-05-03Version 1

For any group G, let C(G) denote the set of centralizers of G. We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n. In this note, we prove that every finite Cn-group with n ? 21 is soluble and this estimate is sharp. Moreover, we prove that every finite Cn-group with |G| < 30n+15 19 is non-nilpotent soluble. This result gives a partial answer to a conjecture raised by A. Ashrafi in 2000.

Comments: to appear in Bulletin of the Iranian Mathematical Society
Categories: math.GR
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