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

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.
Volume 2, Issue 1 - Serial Number 1
Proceedings of the Ischia Group Theory 2012
March 2013
Pages 45-47
  • Receive Date: 01 November 2012
  • Revise Date: 28 December 2012
  • Accept Date: 28 December 2012
  • Published Online: 01 March 2013