Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Width of Verbal Subgroups of the Groups of Triangular Matrices
  over a Field of Arbitrary Characteristic   The width $\wid(G,W)$ of the verbal subgroup $v(G,W)$ of a group $G$ defined
by a collection of group words $W$ is the smallest number $m$ in $\mathbb N
\cup {+\infty}$ such that every element of $v(G,W)$ is can be represented as
the product of at most $m$ words in $W$ evaluated on the group $G$ and their
inverses. Recall that every verbal subgroup of the group $T_{n} (K)$ of
triangular matrices over an arbitrary field $K$ can be defined by just one
word: an outer commutator word or a power word. We prove that for every outer
commutator word $w$ the equality $\wid(T_{n} (K),w)=1$ holds on the group
$T_{n} (K)$ and that if $w=x^{s}$ then $\wid(T_{n}(K),w)=1$ except in two
cases:
  (1) the field $K$ is finite and $s$ is divisible by the characteristic $p$ of
$K$ but not by $|K|-1$;
  (2) the field $K$ is finite and $s=p^{t} (|K|-1)^{u} r$ for $r,t,u\in \mathbb
N$ with $n\ge p^{t} +3$, while $r$ not divisible by $p$.
  In these cases the width equals 2. For finitary triangular groups the
situation is similar, but in the second case the restriction $n\ge p^{t} +3$ is
superfluous.

37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an