On the structure of just infinite profinite groups

Details On the structure of just infinite profinite groups On the structure of just infinite profinite groups

2009-06-09

arxiv.org/abs/0906.1771v2

Journal of Algebra Volume 324, Issue 9, 1 November 2010, Pages 2249-2261

Mathematics

Group Theory

16 pages

Scientific paper

10.1016/j.jalgebra.2010.07.034

A profinite group $G$ is just infinite if every closed normal subgroup of $G$ is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup $H$ of $G$, there are only finitely many open normal subgroups of $G$ not contained in $H$. This extends a result recently established by Barnea, Gavioli, Jaikin-Zapirain, Monti and Scoppola, who proved the same characterisation in the case of pro-$p$ groups. We also use this result to establish a number of features of the general structure of profinite groups with regard to the just infinite property.

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