Maximal subgroups of finitely presented special inverse monoids

Gray, Robert and Kambites, Mark (2025) Maximal subgroups of finitely presented special inverse monoids. Journal of the European Mathematical Society. ISSN 1435-9855

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Abstract

We study the maximal subgroups (also known as group H-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and moreover every such maximal subgroup can also arise in the E-unitary case. We also prove that the possible groups of units are exactly the finitely generated recursively presented groups; this improves upon a result of, and answers a question of, the first author and Ruškuc. These results give the first significant insight into the maximal subgroups of such monoids beyond the group of units, and the results together demonstrate that (perhaps surprisingly) it is possible for the subgroup structure to have a complexity which significantly exceeds that of the group of units. We also observe that a finitely presented special inverse monoid (even an E-unitary one) may have infinitely many pairwise non-isomorphic maximal subgroups; this contrasts sharply with the case of (non-inverse) special monoids, where Malheiro showed that all idempotents lie in the D-class of 1, from which it follows that all maximal subgroups are isomorphic.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	LivePure Connector
Date Deposited:	22 Apr 2024 09:30
Last Modified:	14 Feb 2025 16:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/94983
DOI:	10.4171/JEMS/1585

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