VARIETIES WITH XN*=X-N IDENTITY M-GROUPS

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 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.