Rocky Mountain Journal of Mathematics

Galois $p$-groups and Galois modules

Sunil Chebolu, Ján Mináč, and Andrew Schultz

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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

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

First available in Project Euclid: 7 December 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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