About: Locally profinite group

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In mathematics, a locally profinite group is a Hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and totally disconnected. Moreover, a locally profinite group is compact if and only if it is profinite; this explains the terminology. Basic examples of locally profinite groups are discrete groups and the p-adic Lie groups. Non-examples are real Lie groups, which have the no small subgroup property.

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  • Eine lokal proendliche Gruppe ist eine topologische Gruppe, die eine proendliche offene Untergruppe hat. Für lokal proendliche Gruppen können definiert werden. (de)
  • In mathematics, a locally profinite group is a Hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and totally disconnected. Moreover, a locally profinite group is compact if and only if it is profinite; this explains the terminology. Basic examples of locally profinite groups are discrete groups and the p-adic Lie groups. Non-examples are real Lie groups, which have the no small subgroup property. In a locally profinite group, a closed subgroup is locally profinite, and every compact subgroup is contained in an open compact subgroup. (en)
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  • Eine lokal proendliche Gruppe ist eine topologische Gruppe, die eine proendliche offene Untergruppe hat. Für lokal proendliche Gruppen können definiert werden. (de)
  • In mathematics, a locally profinite group is a Hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and totally disconnected. Moreover, a locally profinite group is compact if and only if it is profinite; this explains the terminology. Basic examples of locally profinite groups are discrete groups and the p-adic Lie groups. Non-examples are real Lie groups, which have the no small subgroup property. (en)
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  • Lokal proendliche Gruppe (de)
  • Locally profinite group (en)
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