On groups generated by involutions of a semigroup

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• 作者：James East^a ; ^{J.East@uws.edu.au" class="auth_mail" title="E-mail the corresponding author} ; Thomas E. Nordahl^b ; ^{tenordahl@ucdavis.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20M15 ; 20B25 ; 20B27 ; 20M20
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：445
• 期：Complete
• 页码：136-162
• 全文大小：563 K

文摘

An involution on a semigroup S   (or any algebra with an underlying associative binary operation) is a function α:S→S$\alpha :S\to S$ that satisfies α(xy)=α(y)α(x)$\alpha (xy)=\alpha (y)\alpha (x)$ and α(α(x))=x$\alpha (\alpha (x))=x$ for all x,y∈S$x,y\in S$. The set I(S)$I(S)$ of all such involutions on S   generates a subgroup C(S)=〈I(S)〉$\mathcal{C}(S)=〈I(S)〉$ of the symmetric group Sym(S)$\mathrm{Sym}(S)$ on the set S  . We investigate the groups C(S)$\mathcal{C}(S)$ for certain classes of semigroups S  , and also consider the question of which groups are isomorphic to C(S)$\mathcal{C}(S)$ for a suitable semigroup S.