FACTORIZING PROFINITE GROUPS INTO TWO ABELIAN SUBGROUPS

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 inverse limits of surjective inverse systems. This is a generalization of a recent result by K.H. Hofmann and F.G. Russo. As an application we reprove their generalization of Iwasawaʹs structure theorem for quasihamiltonian pro-p groups.