Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The relative second Fox and third dimension subgroup of arbitrary groups   Let $I_R(G)$ denote the augmentation ideal of the group algebra $R(G)$ of a
group $G$ with coefficients in a commutative ring $R$. We give a complete
description of the third relative dimension subgroup
$G\cap(1+I_R(K)I_R(G)+I^3_R(G))$ and the second relative Fox subgroup
$G\cap(1+I_R(K)I_R(H)+I^2_R(G)I_R(H))$ for any subgroups $K$ and $H$ of $G$.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat