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Commutativity preserving extensions of groups

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

Published online by Cambridge University Press:  20 December 2017

Urban Jezernik  and
Primož Moravec
Urban Jezernik
Affiliation:
Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia (urban.jezernik@imfm.si)
Primož Moravec
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 21, 1000 Ljubljana, Slovenia (primoz.moravec@fmf.uni-lj.si)
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Abstract

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In parallel to the classical theory of central extensions of groups, we develop a version for extensions that preserve commutativity. It is shown that the Bogomolov multiplier is a universal object parametrizing such extensions of a given group. Maximal and minimal extensions are inspected, and a connection with commuting probability is explored. Such considerations produce bounds for the exponent and rank of the Bogomolov multiplier.

Keywords

commutativity preserving extensionBogomolov multipliercommuting probability

MSC classification

Secondary: 20E22: Extensions, wreath products, and other compositions 20J06: Cohomology of groups
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 575 - 592
Copyright
Copyright © Royal Society of Edinburgh 2018