The relative rank of the endomorphism monoid of a finite $G$-set
Autor: | Castillo-Ramirez, Alonso, Ruiz-Medina, Ramón H. |
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Rok vydání: | 2022 |
Předmět: | |
Zdroj: | Published in Semigroup Forum (2023) |
Druh dokumentu: | Working Paper |
DOI: | 10.1007/s00233-023-10340-7 |
Popis: | For a group $G$ acting on a set $X$, let $\text{End}_G(X)$ be the monoid of all $G$-equivariant transformations, or $G$-endomorphisms, of $X$, and let $\text{Aut}_G(X)$ be its group of units. After discussing few basic results in a general setting, we focus on the case when $G$ and $X$ are both finite in order to determine the smallest cardinality of a set $W \subseteq \text{End}_G(X)$ such that $W \cup \text{Aut}_G(X)$ generates $\text{End}_G(X)$; this is known in semigroup theory as the relative rank of $\text{End}_G(X)$ modulo $\text{Aut}_G(X)$. Comment: 15 pages. To appear in Semigroup Forum |
Databáze: | arXiv |
Externí odkaz: | |
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