Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $\mathcal{M}$-supplemented subgroups   Let $G$ be a finite group and $p^k$ be a prime power dividing $|G|$. A
subgroup $H$ of $G$ is called to be $\mathcal{M}$-supplemented in $G$ if there
exists a subgroup $K$ of $G$ such that $G=HK$ and $H_iK<G$ for every maximal
subgroup $H_i$ of $H$. In this paper, we complete the classification of the
finite groups $G$ in which all subgroups of order $p^k$ are
$\mathcal{M}$-supplemented. In particular, we show that if $k\geq 2$, then
$G/\mathrm{O}_{p'}(G)$ is supersolvable with a normal Sylow $p$-subgroup and a
cyclic $p$-complement.

21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg