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Abelianness and centrality in inverse semigroups

Part of: Semigroups Special aspects of infinite or finite groups Algebraic structures

Published online by Cambridge University Press:  09 September 2025

Michael Kinyon Open the ORCID record for Michael Kinyon [Opens in a new window]  and
David Stanovský Open the ORCID record for David Stanovský [Opens in a new window]
Michael Kinyon*
Affiliation:
Department of Mathematics, University of Denver, Denver, CO, USA
David Stanovský
Affiliation:
Department of Algebra, Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic
*
Corresponding author: Michael Kinyon, email: mkinyon@du.edu
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Abstract

We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to conjugation in inverse semigroups. Subsequently, we prove that solvable and nilpotent inverse semigroups are groups.

Keywords

abeliannesscentralityinverse semigroupnilpotencesolvability

MSC classification

Primary: 20M18: Inverse semigroups
Secondary: 20F19: Generalizations of solvable and nilpotent groups 08A30: Subalgebras, congruence relations

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 17
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Edinburgh Mathematical Society.

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