TY - JOUR
ID - 427
TI - On solubility of groups with finitely many centralizers
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Zarrin, M.
AD - University of Kurdistan
Y1 - 2013
PY - 2013
VL - 39
IS - 3
SP - 517
EP - 521
KW - centralizer
KW - n-centralizer group
KW - soluble group
DO -
N2 - 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
UR - http://bims.iranjournals.ir/article_427.html
L1 - http://bims.iranjournals.ir/article_427_8d03882cd4079696032e9bedcf5e7396.pdf
ER -