Commutativity preserving extensions of groups

2015/10/06 by Jezernik, Urban, Moravec, Primoz · 1 citation
#20E22 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1510.01536

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.

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