Maximal Subsemigroups of Infinite Symmetric Inverse Monoids

2025/09/10 by M. Hampenberg, Hampenberg, M., Y. Péresse +1
Computer Science · Mathematics · #03E75 (Secondary) #20E28 #20M20 (Primary) 20M18 #Advanced Algebra and Logic #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2509.08468

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The symmetric inverse monoid I_X on a set X consists of all bijective functions whose domain and range are subsets of X under the usual composition and inversion of partial functions. For an arbitrary infinite set X, we classify all maximal subsemigroups and maximal inverse subsemigroups of I_X which contain the symmetric group Sym(X) or any of the following subgroups of Sym(X): the pointwise stabiliser of a finite subset of X, the stabiliser of an ultrafilter on X, or the stabiliser of a partition of X into finitely many parts of equal cardinality.

Citations

• Submonoids of Infinite Symmetric Inverse Monoids
• Maximal subsemigroups of the semigroup of all mappings on an infinite set
• Maximal clones on uncountable sets that include all permutations

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• Submonoids of Infinite Symmetric Inverse Monoids
• Maximal subsemigroups of the semigroup of all mappings on an infinite set
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