Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finiteness of some verbal subgroups in profinite groups   Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is
denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$.
In the present paper we consider profinite groups admitting a word $w$ such
that the cardinality of $G_w$ is less than $2^{\aleph_0}$ and $w(G)$ is
generated by finitely many $w$-values. For several families of words $w$ we
show that under these assumptions $w(G)$ must be finite. Our results are
related to the concept of conciseness of group words.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph