On a Problem Posed by Belcastro and Sherman

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 1,  2016, pp.121-123
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.1.121
Title & Authors
On a Problem Posed by Belcastro and Sherman
Dutta, Jutirekha;

Abstract
In this paper, we compute the number of distinct centralizers and commutativity degree of a class of finite groups. These computations produce a further class of examples of groups answering one question raised by Belcastro and Sherman and another one raised by Lescot.
Keywords
finite group;centralizer;commutativity degree;
Language
English
Cited by
References
1.
A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloquium, 7(2)(2000), 139-146.

2.
A. R. Ashrafi, Counting the centralizers of some finite groups, Korean J. Comput. & Appl. Math, 7(1)(2000), 115-124.

3.
S. M. Belcastro and G. J. Sherman, Counting centralizers in finite groups, Math. Magazine, 67(5)(1994), 366-374.

4.
A. Castelaz, Commutativity degree of finite groups, M. A. thesis, Wake Forest University, (2010) pp: 72-103, pp: 132.

5.
H. Doostie and M. Maghasedi, Certain classes of groups with commutativity degree d(G) < $\frac{1}{2}$, Ars Combinatoria, 89(2008), 263-270.

6.
I. V. Erovenko and B. Sury, Commutativity degree of wreath products of finite abelian groups, Bull. Aus. Math. Soc., 77(1)(2008), 31-36.

7.
P. Lescot, Central extensions and commutativity degree, Comm. Algebra, 29(10)(2001), 4451-4460.