HS-stability and complex products in involution semigroups

Abstract

AbstractWhen does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing HS-stability and characterising the HS-stable involution subsemigroup generated by a subset of a given involution semigroup. We study HS-stability for the special cases of regular $${}^{*}$$ ∗ -semigroups and commutative involution semigroups.