HS-stability and complex products in involution semigroups

Authors :: Thomas Quinn-Gregson
Nikolaas Verhulst
Bertalan Bodor
Erkko Lehtonen
CMA - Centro de Matemática e Aplicações
Source :: Repositório Científico de Acesso Aberto de Portugal, Repositório Científico de Acesso Aberto de Portugal (RCAAP), instacron:RCAAP, Semigroup Forum, 103(2)
Publication Year :: 2021
Publisher :: Springer Science and Business Media LLC, 2021.
Abstract: 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.<br />Comment: 14 pages

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