Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groups with a solvable subgroup of prime-power index   In this paper we describe some properties of groups $G$ that contain a
solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2--3).
We prove that if $G$ is a non-solvable group that contains a solvable subgroup
of index $p^{\alpha}$ (for some prime $p$), then the quotient $G/\mbox{rad}(G)$
of $G$ over the solvable radical is asymptotically small in comparison to
$p^{\alpha}!$ (Theorem 4).

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ