About: Totally disconnected group

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Totally disconnected group Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Group100031264, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FTotally_disconnected_group

In mathematics, a totally disconnected group is a topological group that is totally disconnected. Such topological groups are necessarily Hausdorff. Interest centres on locally compact totally disconnected groups (variously referred to as groups of td-type, locally profinite groups, or t.d. groups). The compact case has been heavily studied – these are the profinite groups – but for a long time not much was known about the general case. A theorem of van Dantzig from the 1930s, stating that every such group contains a compact open subgroup, was all that was known. Then groundbreaking work on this subject was done in 1994, when showed that every locally compact totally disconnected group contains a so-called tidy subgroup and a special function on its automorphisms, the scale function, ther

Attributes	Values
rdf:type	yago:WikicatTopologicalGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label	完全不連結群 (ja) Totally disconnected group (en)
rdfs:comment	数学において、完全非連結群(totally disconnected group)とは完全非連結な位相群のことである。完全非連結群はハウスドルフである。局所コンパクトな完全非連結群（td-型の群、局所副有限群、t.d.群, TDLC群などと呼ばれる)は興味深い対象である。完全非連結群がコンパクトである場合、すなわち副有限群である場合については十分に研究されてきたが、長い間その一般的な場合である局所コンパクトな完全非連結群についてはあまり知られていなかった。1930年代では「局所コンパクトな完全非連結群はコンパクト開部分群をもつ」というの定理が知られているのみであった。局所コンパクトな完全非連結群に関する画期的な業績は1994年になされた;は、任意の局所コンパクト完全非連結群は"整然部分群"と、"スケール関数"と呼ばれる整然部分群の自己同型写像上の特殊な関数（定義は後述）を持つことを示し、これによって局所的な完全非連結群の構造に関する知識が向上した。完全非連結群の大域的な構造に関する進歩は2011年にCapraceとMonodによって得られ、その中でもとそのの分類は際立ったものである。 (ja) In mathematics, a totally disconnected group is a topological group that is totally disconnected. Such topological groups are necessarily Hausdorff. Interest centres on locally compact totally disconnected groups (variously referred to as groups of td-type, locally profinite groups, or t.d. groups). The compact case has been heavily studied – these are the profinite groups – but for a long time not much was known about the general case. A theorem of van Dantzig from the 1930s, stating that every such group contains a compact open subgroup, was all that was known. Then groundbreaking work on this subject was done in 1994, when showed that every locally compact totally disconnected group contains a so-called tidy subgroup and a special function on its automorphisms, the scale function, ther (en)
dcterms:subject	Topological groups
Wikipage page ID	4947490 (xsd:integer)
Wikipage revision ID	1118417836 (xsd:integer)
Link from a Wikipage to another Wikipage	Nicolas Monod David van Dantzig Characteristically simple group Lie group Profinite group Compact space Mathematics Neighbourhood (mathematics) Totally disconnected Locally compact Compositio Mathematica Mathematische Annalen Subgroup Automorphism Topological groups Topological group Hausdorff space Locally profinite group American Mathematical Society Noetherian group Inner automorphism Neighbourhood basis Open set Math. Proc. Cambridge Philos. Soc. Springer-Verlag P-adic dbr:George_Willis_(mathematician)
Link from a Wikipage to an external page	http://www.numdam.org/item%3Fid=CM_1936__3__408_0 http://www.ams.org/online_bks/pspum331/pspum331-ptI-7.pdf http://www.digizeitschriften.de/dms/resolveppn/%3FPID=GDZPPN002339951
sameAs	Totally disconnected group Totally disconnected group Totally disconnected group Totally disconnected group Totally disconnected group
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Main dbt:Reflist
has abstract	In mathematics, a totally disconnected group is a topological group that is totally disconnected. Such topological groups are necessarily Hausdorff. Interest centres on locally compact totally disconnected groups (variously referred to as groups of td-type, locally profinite groups, or t.d. groups). The compact case has been heavily studied – these are the profinite groups – but for a long time not much was known about the general case. A theorem of van Dantzig from the 1930s, stating that every such group contains a compact open subgroup, was all that was known. Then groundbreaking work on this subject was done in 1994, when showed that every locally compact totally disconnected group contains a so-called tidy subgroup and a special function on its automorphisms, the scale function, thereby advancing the knowledge of the local structure. Advances on the global structure of totally disconnected groups were obtained in 2011 by Caprace and Monod, with notably a classification of characteristically simple groups and of Noetherian groups. (en) 数学において、完全非連結群(totally disconnected group)とは完全非連結な位相群のことである。完全非連結群はハウスドルフである。局所コンパクトな完全非連結群（td-型の群、局所副有限群、t.d.群, TDLC群などと呼ばれる)は興味深い対象である。完全非連結群がコンパクトである場合、すなわち副有限群である場合については十分に研究されてきたが、長い間その一般的な場合である局所コンパクトな完全非連結群についてはあまり知られていなかった。1930年代では「局所コンパクトな完全非連結群はコンパクト開部分群をもつ」というの定理が知られているのみであった。局所コンパクトな完全非連結群に関する画期的な業績は1994年になされた;は、任意の局所コンパクト完全非連結群は"整然部分群"と、"スケール関数"と呼ばれる整然部分群の自己同型写像上の特殊な関数（定義は後述）を持つことを示し、これによって局所的な完全非連結群の構造に関する知識が向上した。完全非連結群の大域的な構造に関する進歩は2011年にCapraceとMonodによって得られ、その中でもとそのの分類は際立ったものである。 (ja)
prov:wasDerivedFrom	wikipedia-en:Totally_disconnected_group?oldid=1118417836&ns=0
page length (characters) of wiki page	5913 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Totally_disconnected_group
is Link from a Wikipage to another Wikipage of	Nicolas Monod Totally disconnected groups Lie group Profinite group Identity component Admissible representation Topological group Locally profinite group Hilbert's fifth problem Totally disconnected space Group of td-type Group of td type T.d. group
is Wikipage redirect of	Totally disconnected groups Group of td-type Group of td type T.d. group
is foaf:primaryTopic of	wikipedia-en:Totally_disconnected_group

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (61 GB total memory, 49 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software