Free subgroups of one-relator relative presentations

被引：3

作者：

Klyachko, A. A. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

ALGEBRA AND LOGIC | 2007年 / 46卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

relative presentations; one-relator groups; free subgroups;

D O I：

10.1007/s10469-007-0015-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that G is a non-trivial torsion-free group and w is a word over the alphabet G boolean OR {x(1)(+/- 1),..., x(n)(+/- 1)}. It is proved that, for n >= 2, the group (G) over tilde = < G, x(1), x(2),..., x(n) | w = 1 > always contains a non-Abelian free subgroup. For n = 1, the question whether there exist non-Abelian free subgroups in (G) over tildeG is amply settled for the unimodular case (i.e., where the exponent sum of x(1) in w is one). Some generalizations of these results are discussed.

引用

页码：158 / 162

页数：5

共 25 条

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