Anisimov's Theorem for inverse semigroups
Group Theory
2013-03-22 v1 Formal Languages and Automata Theory
Abstract
The idempotent problem of a finitely generated inverse semigroup is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent problem is necessarily finite. This answers a question of Gilbert and Noonan Heale, and establishes a generalisation to inverse semigroups of Anisimov's Theorem for groups.
Cite
@article{arxiv.1303.5239,
title = {Anisimov's Theorem for inverse semigroups},
author = {Mark Kambites},
journal= {arXiv preprint arXiv:1303.5239},
year = {2013}
}
Comments
8 pages