Cardinalities in finite monoids of $G$-equivariant functions
Group Theory
2025-03-07 v1
Abstract
A set with a group action is referred to as a -set, and the set of functions that commute with this action forms a monoid under function composition. This paper examines the case where the -set is finite, which implies that the monoid of -equivariant functions is also finite. The document provides formulas for calculating the cardinality of this monoid, its group of units, and explores special cases of -equivariant functions, known as fixing elementary collapsings. All of these results are expressed in terms of specific properties of the -set, including the number of orbits and certain indices of the subgroups acting as stabilizers.
Keywords
Cite
@article{arxiv.2503.03772,
title = {Cardinalities in finite monoids of $G$-equivariant functions},
author = {Ramón H. Ruiz-Medina},
journal= {arXiv preprint arXiv:2503.03772},
year = {2025}
}