Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elements of uniformly bounded word-length in groups   We study a characteristic subgroup of finitely generated groups, consisting
of elements with uniform upper bound for word-lengths. For a group $G$, we
denote this subgroup by $G_{bound}$. We give sufficient criteria for triviality
and finiteness of $G_{bound}$. We prove that if $G$ is virtually abelian then
$G_{bound}$ is finite. In contrast with numerous examples where $G_{bound}$ is
trivial, we show that for every finite group $A$, there exists an infinite
group $G$ with $G_{bound}=A$. This group $G$ can be chosen among torsion
groups. We also study the group $G_{bound}(d)$ of elements with uniformly
bounded word-lengths for generating sets of cardinality less than $d$.

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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom