The Sylow subgroups of the absolute Galois group Gal(Q)
Number Theory
2016-10-05 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1403.3266,
title = {The Sylow subgroups of the absolute Galois group Gal(Q)},
author = {Lior Bary-Soroker and Moshe Jarden and Danny Neftin},
journal= {arXiv preprint arXiv:1403.3266},
year = {2016}
}