Rocky Mountain Journal of Mathematics

Galois $p$-groups and Galois modules

Sunil Chebolu, Ján Mináč, and Andrew Schultz

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Abstract

The smallest non-abelian $p$-groups play a fundamental role in the theory of Galois $p$-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups--as well as other closely related, larger $p$-groups--occur as Galois groups over given base fields. We show further how the appearance of some Galois groups forces the appearance of other Galois groups in an interesting way.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 5 (2016), 1405-1446.

Dates
First available in Project Euclid: 7 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1481101219

Digital Object Identifier
doi:10.1216/RMJ-2016-46-5-1405

Mathematical Reviews number (MathSciNet)
MR3580794

Zentralblatt MATH identifier
06663618

Subjects
Primary: 12F10: Separable extensions, Galois theory
Secondary: 12F12: Inverse Galois theory

Keywords
Galois groups $p$-groups Galois modules enumerating Galois extensions norm residue isomorphism

Citation

Chebolu, Sunil; Mináč, Ján; Schultz, Andrew. Galois $p$-groups and Galois modules. Rocky Mountain J. Math. 46 (2016), no. 5, 1405--1446. doi:10.1216/RMJ-2016-46-5-1405. https://projecteuclid.org/euclid.rmjm/1481101219


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