Free subgroups of one-relator relative presentations

Details Free subgroups of one-relator relative presentations Free subgroups of one-relator relative presentations

2005-10-26

arxiv.org/abs/math/0510582v3

Algebra i Logika, 2007, 46:3, 290-298

Mathematics

Group Theory

V3: A small correction in the last phrase of the proof of Theorem 1. 4 pages

Scientific paper

10.1007/s10469-007-0015-1

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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