Galois realizability of groups of orders p
                     5 and p
                     6

Michailov, Ivo M.

doi:10.2478/s11533-013-0217-9

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…We proved similar results for p-groups in [10,11,12,13]. Moreover, we were able to find the obstructions for any group of nilpotency class ≤ 2.…”

Section: Fig 2 Action Of Complex Conjugationsupporting

confidence: 80%

Contemporary Galois theory and its classical problems

Michailov

2023

MEM

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In this survey we outline the milestones of several classical problems in Galois theory: Noether’s problem, the inverse problem and the embedding problem. We demonstrate the connection between these problems in the bigger context of the invariant theory of finite groups. We also point out several new results of the author and his collaborators regarding Noether’s problem and the embedding problem.

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“…We proved similar results for p-groups in [10,11,12,13]. Moreover, we were able to find the obstructions for any group of nilpotency class ≤ 2.…”

Section: Fig 2 Action Of Complex Conjugationsupporting

confidence: 80%

Contemporary Galois theory and its classical problems

Michailov

2023

MEM

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“…Only relatively recently, the investigations of the Galois realizability of some larger p-groups among families of small p-groups, appeared. (See the very interesting papers [Mi1], [Mi2], [GS].) In these papers the main concern is understanding cohomological and Brauer group obstructions for the realizability of Galois field extensions with prescribed Galois groups.…”

Section: Introductionmentioning

confidence: 99%

Construction of unipotent Galois extensions and Massey products

Mináč

Tân

2017

Advances in Mathematics

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For all primes p and for all fields, we find a sufficient and necessary condition of the existence of a unipotent Galois extension of degree p 6 . The main goal of this paper is to describe an explicit construction of such a Galois extension over fields admitting such a Galois extension. This construction is surprising in its simplicity and generality. The problem of finding such a construction has been left open since 2003. Recently a possible solution of this problem gained urgency because of an effort to extend new advances in Galois theory and its relations with Massey products in Galois cohomology.

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“…The groups of orders p 5 and p 6 that have abelian quotients obtained by factoring out µ p or (µ p ) 2 will be investigated in a future paper by Michailov [Mi9].…”

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confidence: 99%

On Galois cohomology and realizability of 2-groups as Galois groups

Michailov

2011

centr.eur.j.math.

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In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related topics.

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Galois realizability of groups of orders p 5 and p 6

Cited by 4 publications

References 15 publications

Contemporary Galois theory and its classical problems

Contemporary Galois theory and its classical problems

Construction of unipotent Galois extensions and Massey products

On Galois cohomology and realizability of 2-groups as Galois groups

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