Inverse semigroups with idempotent-fixing automorphisms

Araújo, João; Kinyon, Michael

http://hdl.handle.net/10400.2/3783

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Authors

Araújo, João

Kinyon, Michael

Abstract(s)

A celebrated result of J. Thompson says that if a finite group G has a fixedpoint-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.

Keywords

Inverse semigroup Automorphism group

URI

http://hdl.handle.net/10400.2/3783

Citation

Araújo, João; Kinyon, Michael - Inverse semigroups with idempotent-fixing automorphisms. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 89, nº 2 (2014), p. 1-6