Unramified alternating extensions of quadratic fields

Details Unramified alternating extensions of quadratic fields Unramified alternating extensions of quadratic fields

2001-03-30

arxiv.org/abs/math/0103234v1

Mathematics

Number Theory

4 pages

Scientific paper

We exhibit, for n at least 5, infinitely many quadratic number fields
admitting unramified degree n extensions with prescribed signature whose normal
closures have Galois group A_n. This generalizes a result of Uchida and
Yamamoto, which did not include the ability to restrict the signature, and a
result of Yamamura, which was the case n=5.

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