Free subgroups of one-relator relative presentations
| dc.creator | Klyachko, Anton A. | |
| dc.date | 2005-10-26 | |
| dc.date | 2006-03-14 | |
| dc.date.accessioned | 2026-07-07T08:26:46Z | |
| dc.date.available | 2026-07-07T08:26:46Z | |
| dc.description | 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=<G,x_1,x_2,...,x_n | w=1> 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. | |
| dc.description | V3: A small correction in the last phrase of the proof of Theorem 1. 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510582 | |
| dc.identifier | http://arxiv.org/abs/math/0510582 | |
| dc.identifier | Algebra i Logika, 2007, 46:3, 290-298 | |
| dc.identifier | doi:10.1007/s10469-007-0015-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137052 | |
| dc.subject | Group Theory | |
| dc.subject | 20F05, 20E06, 20E07 | |
| dc.title | Free subgroups of one-relator relative presentations | |
| dc.type | text |