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arXiv · 1403.3266

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

Lior Bary-Soroker·Moshe Jarden·Danny Neftin
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Abstract

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

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Lior Bary-Soroker, Moshe Jarden, Danny Neftin. 2014-03-13. The Sylow subgroups of the absolute Galois group Gal(Q). https://arxiv.org/abs/1403.3266

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