Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak second maximal subgroups in solvable groups   In this paper, we investigate the difference between weak second maximal
subgroups and second maximal subgroups. A sufficient and necessary condition is
also given to describe such class of groups whose weak second maximal subgroups
coincide with its second maximal subgroups(called WSM-groups) under the
solvable case. As an application, we show that every non-vanishing element of a
solvable WSM-group lies in its Fitting subgroup.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph