On Restricting Subsets of Bases in Relatively Free Groups

Details On Restricting Subsets of Bases in Relatively Free Groups On Restricting Subsets of Bases in Relatively Free Groups

2011-03-15

arxiv.org/abs/1103.2992v2

Mathematics

Group Theory

7 pages; substantially revised with more cases added and some proofs simplified; to appear in IJAC

Scientific paper

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 A_mA_n, and let A = {a_1,..., a_r} 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 {a_{l+1},...,a_r}, then S is a subset of a basis for the relatively free group on {a_1,...,a_l}.

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