Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the length of finite factorized groups   The nonsoluble length $\lambda (G)$ of a finite group $G$ is defined as the
number of nonsoluble factors in a shortest normal series each of whose factors
either is soluble or is a direct product of nonabelian simple groups. The
generalized Fitting height of a finite group $G$ is the least number $h=h^*(G)$
such that $F^*_h(G)=G$, where $F^*_1(G)=F^*(G)$ is the generalized Fitting
subgroup, and $F^*_{i+1}(G)$ is the inverse image of $F^*(G/F^*_{i}(G))$. It is
proved that if a finite group $G=AB$ is factorized by two subgroups of coprime
orders, then the nonsoluble length of $G$ is bounded in terms of the
generalized Fitting heights of $A$ and $B$. It is also proved that if, say, $B$
is soluble of derived length $d$, then the generalized Fitting height of $G$ is
bounded in terms of $d$ and the generalized Fitting height of $A$.

11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics