Transformation representations of sandwich semigroups

2018/03/02 by East, James
#FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1803.00724

Abstract

Let a be an element of a semigroup S. The local subsemigroup of S with respect to a is the subsemigroup aSa of S. The variant of S with respect to a is the semigroup with underlying set S and operation ⋆_a defined by x⋆_ay=xay for x,y∈ S. We show that the following classes contain precisely the same semigroups, up to isomorphism: all local subsemigroups of all finite full transformation semigroups; and all variants of all finite full transformation semigroups. This result was discovered as a result of some experiments (and accidents) when working with the Semigroups package for GAP.

Related

• Local subsemigroups and variants of some class of semigroups
• Sandwich semigroups in locally small categories II: Transformations
• Sandwich semigroups in locally small categories I: Foundations
• The automorphism group of the sandwich inverse symmetric semigroup
• Enumerating Transformation Semigroups