Commutativity preserving extensions of groups

TL;DR

This paper develops a theory of commutativity-preserving group extensions, linking the Bogomolov multiplier to universal parametrization, and explores bounds related to commuting probability.

Contribution

It introduces a new framework for commutativity-preserving extensions and connects it to the Bogomolov multiplier, providing bounds and structural insights.

Findings

Bogomolov multiplier parametrizes commutativity-preserving extensions

Bounds established for the exponent and rank of the multiplier

Connections made between extensions and commuting probability

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.