Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On words that are concise in residually finite groups   A group-word w is called concise if whenever the set of w-values in a group G
is finite it always follows that the verbal subgroup w(G) is finite. More
generally, a word w is said to be concise in a class of groups X if whenever
the set of w-values is finite for a group $G\in X$, it always follows that w(G)
is finite. P. Hall asked whether every word is concise. Due to Ivanov the
answer to this problem is known to be negative. Dan Segal asked whether every
word is concise in the class of residually finite groups. In this direction we
prove that if w is a multilinear commutator and q is a prime-power, then the
word $w^q$ is indeed concise in the class of residually finite groups. Further,
we show that in the case where $w=\gamma_{k}$ the word $w^q$ is boundedly
concise in the class of residually finite groups. It remains unknown whether
the word $w^q$ is actually concise in the class of all groups.

26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th