Systems of elements preserving measure on varieties of groups

Abstract

It is proved that for any , , a system of elements of a free metabelian group of rank is primitive if and only if it preserves measure on the variety of metabelian groups . From this we obtain the result that a system of elements is primitive in the group if and only if it is primitive in its profinite completion . Furthermore, it is proved that there exist a variety and a nonprimitive element such that preserves measure on .Bibliography: 13 titles.