Partial automorphism semigroups

Decidability and Tameness in the Theory of Finite Semigroups

Automorphisms of partial endomorphism semigroups

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...

Computing automorphisms of semigroups

In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As an application of the algorithm, all the automorphism groups of semigroup of order at most 7 and of the multiplicative semigroups of some group rings ar...

On the structure of two generalizations of the full inverse symmetric semigroup

We introduce two generalizations of the full inverse symmetric semigroup ISX — the inverse semigroups PIPX and P̃IPX . Both of these semigroups have the same set of elements and contain ISX . The binary operations on PIPX and P̃IPX are two natural generalizations of the multiplication of partial permutations and each of the considered operations coincides with this multiplication when restricted ...

The semigroups of order 9 and their automorphism groups

We report the number of semigroups with 9 elements up to isomorphism or anti-isomorphism to be 52 989 400 714 478 and up to isomorphism to be 105 978 177 936 292. We obtained these results by combining computer search with recently published formulae for the number of nilpotent semigroups of degree 3. We further provide a complete account of the automorphism groups of the semigroups with at mos...