A note on \(\omega\)-permutable semigroups (Q1262957)
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scientific article; zbMATH DE number 4125703
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on \(\omega\)-permutable semigroups |
scientific article; zbMATH DE number 4125703 |
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A note on \(\omega\)-permutable semigroups (English)
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1990
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It is proved that a finitely generated and periodic semigroup S is finite iff S is \(\omega\)-permutable. The last one means that for any infinite sequence \(s_ i\in S\) there exist \(n>1\) and a non-trivial permutation \(\sigma \in S_ n\) such that \[ s_ 1s_ 2...s_ n=s_{\sigma (1)}s_{\sigma (2)}...s_{\sigma (n)}. \] Some related results are discussed.
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finitely generated
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periodic semigroup
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\(\omega\)-permutable
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0.9261435
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0.92330563
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0.9184297
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0.90128064
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