Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorizations of finite groups by conjugate subgroups which are
  solvable or nilpotent   We consider factorizations of a finite group $G$ into conjugate subgroups,
$G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$,
where $A$ is nilpotent or solvable. First we exploit the split $BN$-pair
structure of finite simple groups of Lie type to give a unified self-contained
proof that every such group is a product of four or three unipotent Sylow
subgroups. Then we derive an upper bound on the minimal length of a solvable
conjugate factorization of a general finite group. Finally, using conjugate
factorizations of a general finite solvable group by any of its Carter
subgroups, we obtain an upper bound on the minimal length of a nilpotent
conjugate factorization of a general finite group.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg