Affiliation:
1. Department of Mathematics Faculty of Sciences University of Zanjan P.O.Box 45371-38791 , Zanjan Iran
Abstract
Abstract
A finite group G is called an F-group (G ∈ F) if for every x, y ∈ G ∖ Z(G), C
G
(x) ≤ C
G
(y) implies that C
G
(x) = C
G
(y). An important subclass of F-groups are CA-groups, consisting of groups in which all centralizers of noncentral elements are abelian. In this paper, among other results, we find the number of element centralizers and the maximum cardinality of subsets of pairwise non-commuting elements in an F-group G with |
G
Z
(
G
)
$\frac{G}{Z(G)}$
| = p
4 for some prime p.
Reference30 articles.
1. Abdollahi, A.—Jafarian Amiri, S. M.—Mohammadi Hassanabadi, A.: Groups with specific number of centralizers, Houston J. Math. 33 (2007), 43–57.
2. Abdollahi, A.—Akbari, S.—Maimani, H. R.: Non-commuting graph of a group, J. Algebra 298 (2006), 468–492.10.1016/j.jalgebra.2006.02.015
3. Ashrafi, A. R.: On finite groups with a given number of centralizers, Algebra Colloq. 7 (2000), 139–146.10.1007/s10011-000-0139-5
4. Azad, A.—Iranmanesh, M. A.—Praeger, C. E.—Spiga, P.: Abelian coverings of finite general linear groups and an application to their non-commuting graphs, J. Algebraic Comb. 34 (2011), 683–710.10.1007/s10801-011-0288-2
5. Azad, A.—Praeger, C. E.: Maximal subsets of pairwise non-commuting elements of three-dimensional general linear groups, Bull. Aus. Math. Soc. 80 (2009), 91–104.10.1017/S0004972709000057
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献