Restivo, Antonio; Reutenauer, Christophe On the Burnside problem for semigroups. (English) Zbl 0545.20051 J. Algebra 89, 102-104 (1984). 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 Cited in 10 ReviewsCited in 45 Documents MSC: 20M10 General structure theory for semigroups 20M05 Free semigroups, generators and relations, word problems Keywords:Burnside problem; finitely generated semigroup; permutation property PDF BibTeX XML Cite \textit{A. Restivo} and \textit{C. Reutenauer}, J. Algebra 89, 102--104 (1984; Zbl 0545.20051) Full Text: DOI References: [1] Herstein, I. N., Noncommutative rings, (Carus Math. Monographs (1969), Math. Assoc. Amer: Math. Assoc. Amer Washington, D. C), Chap. 8 · Zbl 0874.16001 [2] Lothaire, M., Combinatorics on Words (1983), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0514.20045 [3] Morse, M.; Hedlund, G., Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J., 11, 1-7 (1944) · Zbl 0063.04115 [4] Rowen, L. H., Polynomial Identities in Ring Theory (1980), Academic Press: Academic Press New York/London · Zbl 0461.16001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.