The Sylow subgroups of the absolute Galois group Gal(Q)

Lior Bary-Soroker; Moshe Jarden; Danny Neftin

doi:10.1016/j.aim.2015.05.017

The Sylow subgroups of the absolute Galois group Gal(Q)

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We describe the ℓ-Sylow subgroups of Gal(Q) for an odd prime ℓ, by observing and studying their decomposition as F⋊Zℓ, where F is a free pro- ℓ group, and Zℓ are the ℓ-adic integers. We determine the finite Zℓ-quotients of F and more generally show that every split embedding problem of Zℓ-groups for F is solvable. Moreover, we analyze the Zℓ-action on generators of F.

Original language	English
Pages (from-to)	186-212
Number of pages	27
Journal	Advances in Mathematics
Volume	284
DOIs	https://doi.org/10.1016/j.aim.2015.05.017
State	Published - 2 Oct 2015

Keywords

Absolute Galois group
Embedding problems
Large fields

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2015.05.017

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abstract = "We describe the ℓ-Sylow subgroups of Gal(Q) for an odd prime ℓ, by observing and studying their decomposition as F⋊Zℓ, where F is a free pro- ℓ group, and Zℓ are the ℓ-adic integers. We determine the finite Zℓ-quotients of F and more generally show that every split embedding problem of Zℓ-groups for F is solvable. Moreover, we analyze the Zℓ-action on generators of F.",

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author = "Lior Bary-Soroker and Moshe Jarden and Danny Neftin",

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AU - Jarden, Moshe

AU - Neftin, Danny

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N2 - We describe the ℓ-Sylow subgroups of Gal(Q) for an odd prime ℓ, by observing and studying their decomposition as F⋊Zℓ, where F is a free pro- ℓ group, and Zℓ are the ℓ-adic integers. We determine the finite Zℓ-quotients of F and more generally show that every split embedding problem of Zℓ-groups for F is solvable. Moreover, we analyze the Zℓ-action on generators of F.

AB - We describe the ℓ-Sylow subgroups of Gal(Q) for an odd prime ℓ, by observing and studying their decomposition as F⋊Zℓ, where F is a free pro- ℓ group, and Zℓ are the ℓ-adic integers. We determine the finite Zℓ-quotients of F and more generally show that every split embedding problem of Zℓ-groups for F is solvable. Moreover, we analyze the Zℓ-action on generators of F.

KW - Absolute Galois group

KW - Embedding problems

KW - Large fields

UR - https://www.scopus.com/pages/publications/84939217232

U2 - 10.1016/j.aim.2015.05.017

DO - 10.1016/j.aim.2015.05.017

M3 - Article

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VL - 284

SP - 186

EP - 212

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The Sylow subgroups of the absolute Galois group Gal(Q)

Abstract

Keywords

ASJC Scopus subject areas

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