Epimorphically closed permutative varieties
Noor Mohammad Khan · Transactions of the American Mathematical Society · 1985
We show that for semigroups all permutation identities are preserved under epis and that all subvarieties of the permutative variety defined by any permutation identity \[ {x_1}{x_2} \cdots {x_n} = {x_{{i_1}}}{x_{{i_2}}} \cdots {x_{{i_n}}},\] with $n \geqslant 3$ and such that ${i_n} e n$ or ${i_1} e 1$, are closed under epis. Finally we find some sufficient conditions that an identity be preserved under epis in conjunction with any nontrivial permutation identity.