Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free subgroups of one-relator relative presentations   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.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th