Counting monogenic monoids and inverse monoids

DOI10.1080/00927872.2023.2214821zbMATH Open1528.20104arXiv2303.12387OpenAlexW4378575025MaRDI QIDQ6094248

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Publication date: 10 October 2023

Published in: Communications in Algebra (Search for Journal in Brave)

Abstract: In this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree $n$ for $n>0$, equals the sum of the number of cyclic subgroups of the symmetric groups on $1$ to $n$ points. We also prove an analogous statement for monogenic subsemigroups of the finite full transformation monoids, as well as monogenic inverse submonoids and subsemigroups of the finite symmetric inverse monoids.

Full work available at URL: https://arxiv.org/abs/2303.12387

zbMATH Keywords

transformation semigroupinverse semigroupmonogenic semigroup

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Inverse semigroups (20M18)

Cites Work

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• Structure of monogenic inverse semigroups
• Enumerating transformation semigroups
• Enumerating finite groups of given order
• Chains of subsemigroups
• Monogenic inverse semigroups and their C* -algebras
• Free Inverse Semigroups

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