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arXiv · 1311.1475

Inverse semigroups with idempotent-fixing automorphisms

Joao Araujo·Michael Kinyon
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Abstract

A celebrated result of J. Thompson says that if a finite group $G$ has a fixed-point-free automorphism of prime order, then $G$ is nilpotent. The main purpose of this note is to extend this result to finite inverse semigroups. An earlier related result of B. H. Neumann says that a uniquely 2-divisible group with a fixed-point-free automorphism of order 2 is abelian. We similarly extend this result to uniquely 2-divisible inverse semigroups.

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Joao Araujo, Michael Kinyon. 2013-11-06. Inverse semigroups with idempotent-fixing automorphisms. https://arxiv.org/abs/1311.1475

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