Subgroups of E-unitary and R1-injective special inverse monoids

Gray, Robert D. and Kambites, Mark (2025) Subgroups of E-unitary and R1-injective special inverse monoids. Mathematische Zeitschrift, 311 (2). ISSN 0025-5874

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Abstract

We continue the study of the structure of general subgroups (in particular maximal subgroups, also known as group H-classes) of special inverse monoids. Recent research of the authors has established that these can be quite wild, but in this paper we show that if we restrict to special inverse monoids which are E-unitary (or have a weaker property we call R1-injectivity), the maximal subgroups are strongly governed by the group of units. In particular, every maximal subgroup has a finite index subgroup which embeds in the group of units. We give a construction to show that every finite group can arise as a maximal subgroup in an R1-injective special inverse monoid with trivial group of units. It remains open whether every combination of a group G and finite index subgroup H can arise as maximal subgroup and group of units.

Item Type:	Article
Additional Information:	Data availability: Not applicable for this paper.
Uncontrolled Keywords:	e-unitary,group h-class,maximal subgroup,r -injective,special inverse monoid,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	01 Jul 2025 09:32
Last Modified:	20 Aug 2025 11:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/99791
DOI:	10.1007/s00209-025-03818-3

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