A note on \(\omega\)-permutable semigroups
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.
scientific article; zbMATH DE number 4125703