A non-solvable Galois extension of $\Q$ ramified at 2 only

Details A non-solvable Galois extension of $\Q$ ramified at 2 only A non-solvable Galois extension of $\Q$ ramified at 2 only

2008-11-26

arxiv.org/abs/0811.4379v2

Mathematics

Number Theory

Scientific paper

In this paper, we show the existence of a non-solvable Galois extension of
$\Q$ which is unramified outside 2. The extension $K$ we construct has degree
$2251731094732800=2^{19}(3\cdot 5\cdot 17\cdot 257)^2$ and has root
discriminant $\delta_K <2^{{47/8}}=58.68...$, and is totally complex.

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