Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-17T17:15:15.651Z Has data issue: false hasContentIssue false
  • English
  • Français

Commutativity preserving extensions of groups

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

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 ([email protected])
Primož Moravec
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 21, 1000 Ljubljana, Slovenia ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)