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commutativity preserving extension

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Commutativity preserving extensions of groups
Part of
- Connections with homological algebra and category theory
- Structure and classification of infinite or finite groups
Urban Jezernik, Primož Moravec
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 3 / June 2018

Published online by Cambridge University Press:

20 December 2017, pp. 575-592

Print publication:

June 2018
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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.