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

2014/03/13 by Bary-Soroker, Lior, Jarden, Moshe, Neftin, Danny · 1 citation
#12E25 #12F10 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.3266

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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