On permutation properties in groups and semigroups
A semigroup S satisfies PPn, the permutation property of degree n (n≥2) if every product of n elements in S remains invariant under some nontrivial permutation of its factors. It is shown that a semigroup satisfies PP3 if and only if it contains at most one nontrivial commutator. Further a regular semigroup is a semilattice of PP3 right or left groups, and a subdirect product of PP3 semigroups of a simple type. A negative answer to a question posed by Restivo and Reutenauer is provided by a suitable PP3 group. © 1987 Springer-Verlag New York Inc.
Garzón, M., & Zalcstein, Y. (1986). On permutation properties in groups and semigroups. Semigroup Forum, 35 (1), 337-351. https://doi.org/10.1007/BF02573115