@article {
author = {Zarrin, M.},
title = {On solubility of groups with finitely many centralizers},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {39},
number = {3},
pages = {517-521},
year = {2013},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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},
keywords = {centralizer,n-centralizer group,soluble group},
url = {http://bims.iranjournals.ir/article_427.html},
eprint = {http://bims.iranjournals.ir/article_427_8d03882cd4079696032e9bedcf5e7396.pdf}
}