Combinatorially Factorizable Cryptic Inverse Semigroups

Abstract

AbstractAn inverse semigroup S is combinatorially factorizable if S = TG where T is a combinatorial (i.e., 𝓗 is the equality relation) inverse subsemigroup of S and G is a subgroup of S. This concept was introduced and studied byMills, especially in the case when S is cryptic (i.e., 𝓗 is a congruence on S). Her approach is mainly analytical considering subsemigroups of a cryptic inverse semigroup.We start with a combinatorial inverse monoid and a factorizable Clifford monoid and from an action of the former on the latter construct the semigroups in the title. As a special case, we consider semigroups that are direct products of a combinatorial inverse monoid and a group.