Generators of Groups and Lie Algebras of the Form F/[N,N]

Abstract

Let F be a free product of nontrivial groups A_i, i ∈ I, and a free group G, and let N be a normal subgroup of F such that N ∩ A_i = 1, i ∈ I. We establish necessary and sufficient conditions for a given element of the group F/[N,N] to belong to the subgroup generated by a given set of elements of F/[N,N] and necessary and sufficient conditions for a given finite set of elements of F/[N,N] to be a set of generators of F/[N,N]. Similar results are obtained for Lie algebras. Bibliography: 10 titles.