Document Type

Article

Publication Date

3-2011

Publication Title

International Journal of Number Theory

Abstract

We present the first explicitly known polynomials in Z[x] with nonsolvable Galois group and field discriminant of the form ±pA for p ≤ 7 a prime. Our main polynomial has degree 25, Galois group of the form PSL2(5)5.10, and field discriminant 569. A closely related polynomial has degree 120, Galois group of the form SL2(5)5.20, and field discriminant 5311. We completely describe 5-adic behavior, finding in particular that the root discriminant of both splitting fields is 125 · 5-1/12500 ≈ 124.984 and the class number of the latter field is divisible by 54.

Volume

7

Issue

2

First Page

289

Last Page

322

DOI

https://doi.org/10.1142/S1793042111004113

ISSN

1793-0421

Comments

Preprint of an article published in International Journal of Number Theory, Volume 7, Issue 2, March 2011, Pages 289-322. https://doi.org/10.1142/S1793042111004113 ©World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijnt

Rights

©World Scientific Publishing Company

Included in

Mathematics Commons

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