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.

中文翻译：

---

对合半群中的 HS 稳定性和复积

一个群的给定数量子集的复积何时生成与其并集相同的子群？我们通过引入 HS 稳定性并表征由给定对合半群的子集生成的 HS 稳定对合子半群，以更一般的形式回答这个问题。我们研究了正则\({}^{*}\) -半群和交换对合半群的特殊情况的 HS 稳定性。