Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On root-class residuality of generalized free products   Root-class residuality of free product of root-class residual groups is
demonstrated. A sufficient condition for root-class residuality of generalized
free product $G$ of groups $A$ and $B$ amalgamating subgroups $H$ and $K$
through the isomorphism $\phi$ is derived. For the particular case when $A=B$,
$H=K$ and $\phi$ is the identity mapping, it is shown that group $G$ is
root-class residual if and only if $A$ is root-class residual and subgroup $H$
of $A$ is root-class closed. These results are extended to generalized free
product of infinitely many groups amalgamating a common subgroup.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat