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Factorizing profinite groups into two abelian subgroups | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 2، شماره 1، خرداد 2013، صفحه 45-47 اصل مقاله (242.38 K) | ||
| نوع مقاله: Ischia Group Theory 2012 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2341 | ||
| نویسنده | ||
| Wolfgang Herfort* | ||
| University of Technology | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| group factorization؛ pro-$p$ groups؛ limits | ||
| مراجع | ||
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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
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