Commutativity preserving extensions of groups
Group Theory
2015-10-07 v1
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 parametrising 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.
Cite
@article{arxiv.1510.01536,
title = {Commutativity preserving extensions of groups},
author = {Urban Jezernik and Primoz Moravec},
journal= {arXiv preprint arXiv:1510.01536},
year = {2015}
}