On varieties of m–groups with identety X_*^n=X^-n

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. An m-group can be regarded as an algebraic system of signature m =<·, e^-1,⋁, ⋀, *> and it is obvious that the m-groups form a variety in this signature. The set M of varieties of all m-groups is a partially ordered set with respect to the set-theoretic inclusion. Moreover, M is a lattice with respect to the naturally defined operations of intersection and union of varieties of m-groups. We study the varieties which is defined by the identity Xⁿ_*=X^-n. We deduce some results on the structure of M.