Counting monogenic monoids and inverse monoids
Group Theory
2023-05-15 v2 Rings and Algebras
Abstract
In this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree for , equals the sum of the number of cyclic subgroups of the symmetric groups on to 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.
Keywords
Cite
@article{arxiv.2303.12387,
title = {Counting monogenic monoids and inverse monoids},
author = {L. Elliott and A. Levine and J. D. Mitchell},
journal= {arXiv preprint arXiv:2303.12387},
year = {2023}
}
Comments
9 pages (2 figures, 1 table, updated with number of improvement, to appear in Comm. Alg.)