Automatic presentations for semigroups

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.

Authors

• Alan J. Cain
• Graham Oliver
• Nik Ruškuc
• Richard M. Thomas

Keywords

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