Inverse semigroups with idempotent-fixing automorphisms

Semigroup Forum, 89(2) (2014), 469-474
http://dx.doi.org/10.1007/s00233-014-9585-0 (Preprint - http://arxiv.org/abs/1311.1475)

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.