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

کلیدواژه ها:

group factorization ، pro-p groups ، limits