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Reconstruction of profinite groups from the closed normal hulls of its Sylow subgroups and natural actions. (English) Zbl 0622.20024

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 \(\{W_ p\}_{p\in {\mathbb{P}}}\).
Reviewer: W.Brauer

MSC:

20E18 Limits, profinite groups
20E22 Extensions, wreath products, and other compositions of groups
20E07 Subgroup theorems; subgroup growth
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References:

[1] Díaz-Barriga, A. J.; López, L. Y., Sumas activas de grupos pro-\(C\), (Anales del Instituto de Matématicas, No. 19-1 (1979), UNAM: UNAM México), 21-40
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