Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subgroup congruences for groups of prime power order   Given a $p$-group $G$ and a subgroup-closed class $\mathfrak{X}$, we
associate with each $\mathfrak{X}$-subgroup $H$ certain quantities which count
$\mathfrak{X}$-subgroups containing $H$ subject to further properties. We show
in Theorem I that each one of the said quantities is always $\equiv 1 \pmod p$
if and only if the same holds for the others. In Theorem II we supplement the
above result by focusing on normal $\mathfrak{X}$-subgroups and in Theorem III
we obtain a sharpened version of a celebrated theorem of Burnside relative to
the class of abelian groups of bounded exponent. Various other corollaries are
also presented.

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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
16
The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th