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- W2181124719 abstract "A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $Gleftthreetimes P,$ where $G$ is a compact topological group and $P$ is a topological subgroup of $Aut(G)$. We prove that $Gleftthreetimes P$ is minimal for every closed subgroup $P$ of $Aut(G)$. In case $G$ is abelian, the same is true for every subgroup $P subseteq Aut(G)$. We show, in contrast, that there exist a compact two-step nilpotent group $G$ and a subgroup $P$ of $Aut(G)$ such that $Gleftthreetimes P$ is not minimal. This answers a question of Dikranjan. Some of our results were inspired by a work of Gamarnik." @default.
- W2181124719 created "2016-06-24" @default.
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- W2181124719 date "2015-11-22" @default.
- W2181124719 modified "2023-09-27" @default.
- W2181124719 title "Minimality of the Semidirect Product" @default.
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