Factorizing profinite groups into two abelian subgroups

Document Type : Ischia Group Theory 2012


University of Technology


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 Iwasawa's structure theorem for‎ ‎quasihamiltonian pro-$p$ groups‎.


Main Subjects

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