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

Lior Bary-Soroker, Moshe Jarden, Danny Neftin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish
Pages (from-to)186-212
Number of pages27
JournalAdvances in Mathematics
StatePublished - 2 Oct 2015


FundersFunder number
National Science FoundationDMS-1303990
German-Israeli Foundation for Scientific Research and Development2289-2241.6/2011


    • Absolute Galois group
    • Embedding problems
    • Large fields


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