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COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS

Part of: Connections with homological algebra and category theory Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 February 2008

IGOR V. EROVENKO  and
B. SURY
IGOR V. EROVENKO
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA (email: igor@uncg.edu)
B. SURY
Affiliation:
Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Rd, Bangalore 560 059, India (email: sury@isibang.ac.in)
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Abstract

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We compute commutativity degrees of wreath products of finite Abelian groups A and B. When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1/n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary number-theoretic result.

Keywords

wreath productcommutativity degree

MSC classification

Secondary: 20E22: Extensions, wreath products, and other compositions 20J06: Cohomology of groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 1 , February 2008 , pp. 31 - 36
Copyright
Copyright © Australian Mathematical Society 2008

References

[1]Lescot, P., ‘Central extensions and commutativity degree’, Comm. Algebra 29 (2001), 4451–4460.CrossRefGoogle Scholar
[2]Meldrum, J. D. P., Wreath products of groups and semigroups, Pitman Monographs and Surveys in Pure and Applied Mathematics, 74 (Longman, Harlow, 1995).Google Scholar