Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bound on the number of ramified primes for odd order solvable
  groups   Let $G$ be a finite group and let $ram^{t}(G)$ denote the minimal positive
integer $n$ such that $G$ can be realized as the Galois group of a tamely
ramified extension of $\mathbb{Q}$ ramified only at $n$ finite primes. Let
$d(G)$ denote the minimal non negative integer for which there exists a subset
$X$ of $G$ with $d(G)$ elements such that the normal subgroup of $G$ generated
by $X$ is all of $G$. It is known that $d(G)\leq ram^{t}(G)$. However, it is
unknown whether or not every finite group $G$ can be realized as a Galois group
of a tamely ramified extension of $\mathbb{Q}$ with exactly $d(G)$ ramified
primes. We will show that $3\cdot log(|G|)$ is an upper bound for $ram^{t}(G)$
for all odd order solvable group $G$.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph