Semigroup Actions, Covering Spaces and Schutzenberger Groups

Details Semigroup Actions, Covering Spaces and Schutzenberger Groups Semigroup Actions, Covering Spaces and Schutzenberger Groups

2009-05-29

arxiv.org/abs/0905.4888v1

Mathematics

Group Theory

Scientific paper

We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results on presentations of Sch\"utzenberger groups. We also give a geometric proof that a finitely generated regular semigroup with finitely many idempotents has polynomial growth if and only if all its maximal subgroups are virtually nilpotent.

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