%0 Journal Article
%T On solubility of groups with finitely many centralizers
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Zarrin, M.
%D 2013
%\ 07/01/2013
%V 39
%N 3
%P 517-521
%! On solubility of groups with finitely many centralizers
%K centralizer
%K n-centralizer group
%K soluble group
%R
%X 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 andthis estimate is sharp. Moreover, we prove that every ﬁnite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashraﬁ in 2000
%U http://bims.iranjournals.ir/article_427_8d03882cd4079696032e9bedcf5e7396.pdf