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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 [email protected]
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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
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. 

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