Views and plexus m-group

Abstract

Recall that an m - group is a pair (G;*); where G is an l - group and * is a decreasing order two automorphism of G: We obtain a description of the m - transitive representations of an arbitrary m - group. Some necessary and suficient conditions are given for an m - group to admit a faithful m - transitive representation. We study the lattice of congruences of an arbitrary m - transitive representation, introduce the notions of m - 2 - transitive and m - primitive representations, and describe the m - transitive primitive representations in terms of stabilizers. Also we give necessary and suficient conditions for m - 2 - transitivity and study some properties of these representations. We introduce the concept of wreath product of the m - groups of permutations and prove that an m - transitive group of permutations with an m - congruence is embeddable into the wreath product of the suitable m - transitive m - groups of permutations. As a consequence, we establish that an arbitrary m - transitive group in the product of two varieties of m - groups embeds into the wreath product of the suitable m - transitive groups of these varieties.