Automatic presentations for semigroups

  • Cain A
  • Oliver G
  • Ruškuc N
 et al. 
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Abstract

This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We give a complete list of FA-presentable one-relation semigroups and compare the classes of FA-presentable semigroups and automatic semigroups. © 2009 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Automatic presentation
  • Cancellative semigroup
  • FA-presentable
  • Virtually abelian group

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