Abstract :
Let p be an odd prime, and let image denote the class of p-groups which occur as Sylow p-subgroups of finite Galois groups over the p-adic field Qp. We prove that image contains every abelian p-group of rank ≤ (p − 1)2, and that certain nonabelian p-groups do not belong to image. For certain number fields K, we show that image coincides with the class of Sylow p-subgroups of K-admissible groups.
