  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.
