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.
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.
Herfort, W. (2013). Factorizing profinite groups into two abelian subgroups. International Journal of Group Theory, 2(1), 45-47. doi: 10.22108/ijgt.2013.2341
MLA
Wolfgang Herfort. "Factorizing profinite groups into two abelian subgroups", International Journal of Group Theory, 2, 1, 2013, 45-47. doi: 10.22108/ijgt.2013.2341
HARVARD
Herfort, W. (2013). 'Factorizing profinite groups into two abelian subgroups', International Journal of Group Theory, 2(1), pp. 45-47. doi: 10.22108/ijgt.2013.2341
VANCOUVER
Herfort, W. Factorizing profinite groups into two abelian subgroups. International Journal of Group Theory, 2013; 2(1): 45-47. doi: 10.22108/ijgt.2013.2341
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