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Statements

Subject Item
dbr:Locally_profinite_group
rdf:type
owl:Thing dbo:Band yago:Group100031264 yago:WikicatTopologicalGroups yago:Abstraction100002137
rdfs:label
Locally profinite group Lokal proendliche Gruppe
rdfs:comment
Eine lokal proendliche Gruppe ist eine topologische Gruppe, die eine proendliche offene Untergruppe hat. Für lokal proendliche Gruppen können definiert werden. 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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dbr:Hecke_algebra_of_a_locally_compact_group
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dbc:Topological_groups
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dbr:Topological_group dbr:Contragredient_representation dbr:No_small_subgroup_property dbr:Local_field dbr:Springer-Verlag dbr:Admissible_representation dbr:Profinite_group dbr:Algebraic_number_theory dbr:Absolute_Galois_group dbr:Hausdorff_space dbr:Discrete_group dbr:Neighbourhood_(topology) dbr:P-adic_Lie_group dbr:Totally_disconnected_group dbc:Topological_groups dbr:Non-Archimedean_ordered_field dbr:General_linear_group dbr:Weil_group dbr:Locally_compact_space dbr:Smooth_representation dbr:Compact_space
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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. 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.
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