Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Number of Sylow subgroups in finite groups   Denote by $\nu_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not
difficult to see that $\nu_p(H)\leq\nu_p(G)$ for $H\leq G$, however $\nu_p(H)$
does not divide $\nu_p(G)$ in general. In this paper we reduce the question
whether $\nu_p(H)$ divides $\nu_p(G)$ for every $H\leq G$ to almost simple
groups. This result substantially generalizes the previous result by G. Navarro
and also provides an alternative proof for the Navarro theorem.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas