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Profinite groups with complemented closed subgroups
Gustavo A. Fern\'andez-Alcober, Giulia Sabatino
https://arxiv.org/abs/2507.20791 https://arxiv.org/…

Profinite groups with complemented closed subgroups
A group $G$ is said to be a $C$-group if every subgroup $H$ has a permutable complement, i.e. if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H \cap K=1$. In this paper, we study the profinite counterpart of this concept. We say that a profinite group $G$ is profinite-$C$ if every closed subgroup admits a closed permutable complement. We first give some equivalent variants of this condition and then we determine the structure of profinite-$C$ groups: they are the semidirect products…