On the Burnside problem for semigroups. (English) Zbl 0545.20051

A finitely generated semigroup S is proved to be finite if and only if S is torsion and possesses the following permutation property: There exists an integer \(n\geq 2\) such that to each \((s_ 1,...,s_ n)\) in \(S^ n\) there corresponds a permutation \(\sigma\) of 1,...,n, \(\sigma \neq id\), so that \(s_ 1s_ 2...s_ n=s_{\sigma(1)}s_{\sigma(2)}...s_{\sigma(n)}.\)
Reviewer: T.J.Harju


20M10 General structure theory for semigroups
20M05 Free semigroups, generators and relations, word problems
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