Galois extensions ramified only at one prime

Details Galois extensions ramified only at one prime Galois extensions ramified only at one prime

2007-12-11

arxiv.org/abs/0712.1653v1

Mathematics

Number Theory

10 pages

Scientific paper

This paper gives some restrictions on finite groups that can occur as Galois groups of extensions over $\Q$ and over $\F_q(t)$ ramified only at one finite prime. Over $\Q$, we strengthen results of Jensen and Yui about dihedral extensions and rule out some non-solvable groups. Over $\F_q(t)$ restrictions are given for symmetric groups and dihedral groups to occur as tamely ramified extension over $\F_q(t)$ ramified only at one prime.

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