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arXiv · 1303.5239

Anisimov's Theorem for inverse semigroups

Mark Kambites
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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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Mark Kambites. 2013-03-21. Anisimov's Theorem for inverse semigroups. https://arxiv.org/abs/1303.5239

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