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Free subgroups of one-relator relative presentations

Anton A. Klyachko
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Abstract

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group G= always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.

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Anton A. Klyachko. 2006-03-14. Free subgroups of one-relator relative presentations. https://doi.org/10.1007/s10469-007-0015-1

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