Abstract

The transformation of normal subgroups of finite index or Corank, satisfying a multilinear commutator identity into characteristic subgroups is presented. The reduction to the nilpotent groups is carried out by using Hall-Higman-type theorems. A characteristic subgroup with a finite index bounded in terms of n, and the weight of the commuter is obtained with the original subgroup having a finite index n. Similar results are proved for a subgroup that satisfies the identity of an arbitrary multilinear commutator, as well as for a nilpotent normal subgroup with a bound for the rank of the quotient group.