Reconstruction of profinite groups from the closed normal hulls of its Sylow subgroups and natural actions (Q1090766)

A result by Tomás on the reconstruction of finite groups as active sums of the normal hulls of their Sylow subgroups is generalized to the profinite case. Let G be a profinite group and \({\mathbb{P}}\) be the set of all primes. For each \(p\in {\mathbb{P}}\) let \(W_ p\) be the closed normal hull of any Sylow p-subgroup of G. Then there is a continuous isomorphism of G onto the active pro-sum of the family \(\{W_ p\}_{p\in {\mathbb{P}}}\).