2018/02/15 by Victoria Gould, Gould, Victoria, Thomas David Quinn-Gregson +1
Computer Science · Mathematics · #semigroups and automata theory #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory
paper · doi:10.48550/arxiv.1802.05703
In this paper we initiate the study of ℵ0-categorical semigroups, where a countable semigroup S is ℵ0-categorical if, for any natural number n, the action of its group of automorphisms Aut S on Sn has only finitely many orbits. We show that ℵ0-categoricity transfers to certain important substructures such as maximal subgroups and principal factors. We examine the relationship between ℵ0-categoricity and a number of semigroup and monoid constructions, namely direct sums, 0-direct unions, semidirect products and P-semigroups. As a corollary, we determine the ℵ0-categoricity of an E-unitary inverse semigroup with finite semilattice of idempotents in terms of that of the maximal group homomorphic image.