[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2016.56.1.121

On a Problem Posed by Belcastro and Sherman

Dutta, Jutirekha (Department of Mathematics, North-Eastern Hill University)

Publication Information

Kyungpook Mathematical Journal / v.56, no.1, 2016 , pp. 121-123 More about this Journal

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;

Citations & Related Records

Reference

1	A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloquium, 7(2)(2000), 139-146. DOI
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. DOI
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. DOI