Minimal nonpermutative pseudovarieties of semigroups. I
Jorge Almeida · Pacific Journal of Mathematics · 1986
A semigroup is permutative if it satisfies an identity of the formwhere σ is a non-identical permutation of {1,2,..., n }.The finite permutative semigroups form a pseudovariety and permutative pseudovarieties enjoy many properties first obtained for commutative pseudovarieties.Several types of permutation identities are considered, and all pseudovarieties minimal with respect to the property of containing a finite semigroup which fails an identity of a given type are determined.This includes the cases of the commutativity identity, the general permutation identities, and the "strong (left) permutation identities".As a preliminary, all minimal non-commutative pseudovarieties of groups and monoids are also determined.