Commutativity preserving extensions of groups
Published online by Cambridge University Press: 20 December 2017
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.
MSC classification
- 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
- 8
- Cited by