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Anisimov's Theorem for inverse semigroups (1303.5239v1)
Published 21 Mar 2013 in math.GR and cs.FL
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.