On Restricting Subsets of Bases in Relatively Free Groups
Abstract
Let G be a finitely generated free, free abelian of arbitrary exponent, free nilpotent, or free solvable group, or a free group in the variety AmAn, and let A = a1,..., ar be a basis for G. We prove that, in most cases, if S is a subset of a basis for G which may be expressed as a word in A without using elements from al+1,...,ar, then S is a subset of a basis for the relatively free group on a1,...,al.
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