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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
Full Text: DOI
[1] Herstein, I.N, Noncommutative rings, (), Chap. 8 · Zbl 0874.16001
[2] Lothaire, M, Combinatorics on words, (1983), 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 New York/London · Zbl 0461.16001
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