Anisimov's Theorem for inverse semigroups

2013/03/21 by Kambites, Mark
#20M18 #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1303.5239

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.

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