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COMMUTATIVITY DEGREE OF A CLASS OF FINITE GROUPS AND CONSEQUENCES

Part of: Probabilistic methods in group theory Representation theory of groups

Published online by Cambridge University Press:  30 January 2013

RAJAT KANTI NATH
RAJAT KANTI NATH*
Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India email rajatkantinath@yahoo.com
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Abstract

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The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. The object of this paper is to compute the commutativity degree of a class of finite groups obtained by semidirect product of two finite abelian groups. As a byproduct of our result, we provide an affirmative answer to an open question posed by Lescot.

Keywords

finite groupscommutativity degree

MSC classification

Secondary: 20D60: Arithmetic and combinatorial problems 20D40: Products of subgroups 20P05: Probabilistic methods in group theory

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 448 - 452
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Ashrafi, A. R., ‘On finite groups with a given number of centralizers’, Algebra Colloq. 7 (2) (2000), 139–146.Google Scholar
Belcastro, S. M. and Sherman, G. J., ‘Counting centralizers in finite groups’, Math. Mag. 67 (5) (1994), 366–374.Google Scholar
Das, A. K. and Nath, R. K., ‘A characterization of certain finite groups of odd order’, Math. Proc. R. Ir. Acad. III (A2) (2011), 69–78.Google Scholar
Erovenko, I. V. and Sury, B., ‘Commutativity degree of wreath products of finite abelian groups’, Bull. Aust. Math. Soc. 77 (1) (2008), 31–36.Google Scholar
Lescot, P., ‘Isoclinism classes and commutativity degrees of finite groups’, J. Algebra 177 (1995), 847–869.CrossRefGoogle Scholar
Lescot, P., ‘Central extensions and commutativity degree’, Comm. Algebra 29 (10) (2001), 4451–4460.Google Scholar
Rusin, D. J., ‘What is the probability that two elements of a finite group commute?’, Pacific J. Math. 82 (1979), 237–247.Google Scholar