# Factorizing profinite groups into two abelian subgroups

Document Type: Ischia Group Theory 2012

Author

University of Technology

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 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.

Keywords

Main Subjects

### References

A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad (2010). Products of finite groups. de Gruyter Expositions in Mathematics, Walter de Gruyter GmbH & Co. KG, Berlin. 53
K. H. Hofmann and P. S. Mostert (1966). Elements of Compact Semigroups. Charles E. Merrill, Columbus, OH.
K. H. Hofmann and F. G. Russo Near Abelian Profinite Groups. Forum Mathematicum, DOI href{http://dx.doi.org/10.1515/forum-2012-0125}{10.1515/forum-2012-0125}..
L. Ribes and P. Zalesskii (2009). Profinite Groups. Spridnger, Berlin, 2nd edition.