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Factorizing profinite groups into two Abelian subgroups

Keywords: group factorization , pro-$p$ groups , limits

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Abstract:

We prove that the class of profinite groups $G$ that have a factorization $G=AB$with $A$ and $B$ abelian closed subgroups, is closed under taking strict projective limits.This is a generalization of a recent result by K.H.~Hofmann and F.G.~Russo.As an application we reprove their generalization of Iwasawa's structure theorem forquasihamiltonian pro-$p$ groups.

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