Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy theory and generalized dimension subgroups   Let $G$ be a group and $R,S,T$ its normal subgroups. There is a natural
extension of the concept of commutator subgroup for the case of three subgroups
$\|R,S,T\|$ as well as the natural extension of the symmetric product $\|\bf
r,\bf s,\bf t\|$ for corresponding ideals $\bf r,\bf s, \bf t$ in the integral
group ring $\mathbb Z[G]$. In this paper, it is shown that the generalized
dimension subgroup $G\cap (1+\|\bf r,\bf s,\bf t\|)$ has exponent 2 modulo
$\|R,S,T\|.$ The proof essentially uses homotopy theory. The considered
generalized dimension quotient of exponent 2 is identified with a subgroup of
the kernel of the Hurewicz homomorphism for the loop space over a homotopy
colimit of classifying spaces.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys