The Sylow subgroups of the absolute Galois group Gal(Q)
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 Zp acting on F, where F is a free pro-p group, and Zp are the p-adic integers. We determine the finite Zp-quotients of F and more generally show that every split embedding problem of Zp-groups for F is solvable. Moreover, we analyze the Zp-action on generators of F.
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