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HS-stability and complex products in involution semigroups

Bodor, Bertalan; Lehtonen, Erkko; Quinn-Gregson, Thomas; Verhulst, Nikolaas

Semigroup Forum, 103 (2021), 395–413

When 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.