e/Finite group

Information
has gloss	eng: In mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of solvable groups and nilpotent groups. A complete determination of the structure of all finite groups is too much to hope for; the number of possible structures soon becomes overwhelming. However, the complete classification of the finite simple groups was achieved, meaning that the "building blocks" from which all finite groups can be built are now known, as each finite group has a composition series.
lexicalization	eng: Finite groups
lexicalization	eng: finite group
subclass of	(noun) any number of entities (members) considered as a unit group, grouping
	Note: 12 other instance(s) ommited in the following list
has instance	e/Alperin-Brauer-Gorenstein theorem
has instance	e/Alternating group
has instance	e/Automorphisms of the symmetric and alternating groups
has instance	e/Cauchy's theorem (group theory)
has instance	e/Cayley table
has instance	e/Central product
has instance	e/Chevalley-Shephard-Todd theorem
has instance	e/Core (group)
has instance	e/Cycle graph (algebra)
has instance	e/Cyclic group
has instance	e/Dihedral group of order 6
has instance	e/Dihedral group
has instance	e/Elementary abelian group
has instance	e/Feit-Thompson theorem
has instance	e/Fourier transform on finite groups
has instance	e/Frobenius group
has instance	e/Hall subgroup
has instance	e/Icosahedral symmetry
has instance	e/Index of a subgroup
has instance	e/List of character tables for chemically important 3D point groups
has instance	e/List of finite simple groups
has instance	e/Local analysis
has instance	e/Octahedral symmetry
has instance	e/Omega and agemo subgroup
has instance	e/PSL(2,7)
has instance	e/Pariah group
has instance	e/Pauli group
has instance	e/Primary cyclic group
has instance	e/Quasidihedral group
has instance	e/Quasithin group
has instance	e/Regular p-group
has instance	e/Representation ring
has instance	e/Representation theory of finite groups
has instance	e/Rubik's cube group
has instance	e/Schreier conjecture
has instance	e/Schur cover
has instance	e/Schur–Zassenhaus theorem
has instance	e/Tetrahedral symmetry
has instance	e/ZJ theorem
has instance	e/fr/Théorème du complément normal de Burnside

Meaning
Arabic
has gloss	ara: الزمرة المنتهية في الرياضيات هي زمرة ذات عدد عناصر منته، بعض نواحي الزمر المحدودة تتم معالجته بعمق في النظرية المحلية ونظرية الزمر القابلة للحل.
lexicalization	ara: زمرة منتهية
Catalan
has gloss	cat: En Matemàtiques, un grup finit és un grup constituït per un nombre finit d'elements, és a dir que el seu cardinal és finit.
lexicalization	cat: grup finit
German
has gloss	deu: Eine endliche Gruppe tritt in der mathematischen Disziplin der Gruppentheorie auf. Endliche Gruppen sind Gruppen, deren Trägermenge M eine endliche Anzahl von Elementen enthält.
lexicalization	deu: endliche Gruppe
Esperanto
lexicalization	epo: Finiaj grupoj
Finnish
has gloss	fin: Ryhmäteoriassa äärellinen ryhmä on ryhmä, jonka alkioiden lukumäärä on äärellinen. Äärellisten ryhmien monet syvälliset teoriat on kehitetty 1900-luvulla. Näistä esimerkkeinä on lokaali teoria, ratkeavien ryhmien teoria ja nilpotentti ryhmä. Vaikka ryhmät ovat äärellisiä, on äärellisten ryhmien teorian tulokset useimmiten liian suuria erikoistapaus kerrallaan tarkastettavaksi.
lexicalization	fin: äärellinen ryhmä
French
has gloss	fra: En mathématiques, un groupe fini est un groupe constitué dun nombre fini déléments, c'est-à-dire que son cardinal est fini.
lexicalization	fra: groupe fini
Italian
has gloss	ita: In matematica un gruppo finito è un gruppo costituito da un numero finito di elementi.
lexicalization	ita: gruppo finito
Korean
has gloss	kor: 유한군(有限群)은 수학적 연구 대상의 일종으로, 군(群)이면서 유한개의 원소를 가지는 것을 말한다. 대수학의 한 분야이다.
lexicalization	kor: 유한군
Dutch
has gloss	nld: In de groepentheorie, een onderdeel van de wiskunde, is een eindige groep een groep die een eindig aantal elementen heeft. Sommige aspecten van de theorie van eindige groepen zijn in twintigste eeuw in groot detail onderzocht, in het bijzonder de lokale theorie, en de theorie van de oplosbare groepen van de nilpotente groepen. Het is echter niet mogelijk om de structuur van alle eindige groepen compleet te bepalen; het aantal mogelijke structuren is daarvoor te groot. Wel is men er in de twintigste eeuw in geslaagd een classificatie van eindige enkelvoudige groepen op te stellen. Deze eindige enkelvoudige groepen kunnen worden gezien als de bepaling van de "bouwblokken" voor alle eindige groepen, aangezien elke groep een compositie series bevat.
lexicalization	nld: eindige groep
Swedish
lexicalization	swe: Ändliga grupper
Vietnamese
has gloss	vie: Nhóm hữu hạn là một nhóm mà số phần tử của nó là hữu hạn. Nhiều khía cạnh về lý thuyết nhóm hữu hạn đã được nghiên cứu kĩ lưỡng trong thế kỉ 20, đặc biệt lý thuyết địa phương, lý thuyết về các nhóm giải được và nhóm lũy linh. Thật sự là khó có thể có một lý thuyết hoàn bị vì sự phức tạp trở nên rất lớn khi khảo sát các nhóm khổng lồ.
lexicalization	vie: Nhóm hữu hạn
Yue Chinese
has gloss	yue: 有限羣（finite group）係指有限集為本嘅羣，佢嘅羣冪元素係有限。循環羣、對稱羣都係其中嘅例。
lexicalization	yue: 有限羣
Chinese
has gloss	zho: 在數學裡，有限群是有著有限多個元素的群。有限群理論中的某些部份在20世紀有著很深的研究，尤其是在局部分析和可解群與冪零群的理論中。期望有個完整的理論是太過火了：其複雜性會隨著群變得越大時而變得壓倒性地巨大。
lexicalization	zho: 有限群

Word:	(case sensitive)
Language:	(ISO 639-3 code, e.g. "eng" for English)

e/Finite group

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