Translator Disclaimer
2018 Realizing 2-groups as Galois groups following Shafarevich and Serre
Peter Schmid
Algebra Number Theory 12(10): 2387-2401 (2018). DOI: 10.2140/ant.2018.12.2387

Abstract

Let G be a finite p-group for some prime p, say of order pn. For odd p the inverse problem of Galois theory for G has been solved through the (classical) work of Scholz and Reichardt, and Serre has shown that their method leads to fields of realization where at most n rational primes are (tamely) ramified. The approach by Shafarevich, for arbitrary p, has turned out to be quite delicate in the case p=2. In this paper we treat this exceptional case in the spirit of Serre’s result, bounding the number of ramified primes at least by an integral polynomial in the rank of G, the polynomial depending on the 2-class of G.

Citation

Download Citation

Peter Schmid. "Realizing 2-groups as Galois groups following Shafarevich and Serre." Algebra Number Theory 12 (10) 2387 - 2401, 2018. https://doi.org/10.2140/ant.2018.12.2387

Information

Received: 26 July 2017; Revised: 21 July 2018; Accepted: 26 August 2018; Published: 2018
First available in Project Euclid: 14 February 2019

zbMATH: 07026821
MathSciNet: MR3911134
Digital Object Identifier: 10.2140/ant.2018.12.2387

Subjects:
Primary: 11R32
Secondary: 20D15

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 10 • 2018
MSP
Back to Top