Abstract
ABSTRACTLet 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.
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