Counting monogenic monoids and inverse monoids

L. Elliott, A. Levine, James David Mitchell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Pages (from-to)4654-4661
Number of pages8
JournalCommunications in Algebra
Issue number11
Early online date23 May 2023
Publication statusPublished - 1 Nov 2023


  • Inverse semigroup
  • Monogenic semigroup
  • Transformation semigroup


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