Abstract
A semigroupS satisfiesPPn, thepermutation property of degree n (n≥2) if every product ofn elements inS remains invariant under some nontrivial permutation of its factors. It is shown that a semigroup satisfiesPP3 if and only if it contains at most one nontrivial commutator. Further a regular semigroup is a semilattice ofPP3 right or left groups, and a subdirect product ofPP3 semigroups of a simple type. A negative answer to a question posed by Restivo and Reutenauer is provided by a suitablePP3 group.
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Communicated by Boris M. Schein
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Garzón, M., Zalcstein, Y. On permutation properties in groups and semigroups. Semigroup Forum 35, 337–351 (1986). https://doi.org/10.1007/BF02573115
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DOI: https://doi.org/10.1007/BF02573115