About: Semidirect product     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.org associated with source document(s)

In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: an inner semidirect product is a particular way in which a group can be constructed from two subgroups, one of which is a normal subgroup, while an outer semidirect product is a Cartesian product as a set, but with a particular multiplication operation. As with direct products, there is a natural equivalence between inner and outer semidirect products, and both are commonly referred to simply as semidirect products.

AttributesValues
rdfs:label
  • Semidirect product
  • Semidirektes Produkt
  • Producto semidirecto
  • Produit semi-direct
  • Prodotto semidiretto
  • 半直積
  • Полупрямое произведение
  • Produto semidireto
  • 半直积
rdfs:comment
  • In der Gruppentheorie, einem Teilgebiet der Mathematik, beschreibt das semidirekte Produkt (manchmal auch halbdirektes Produkt) eine spezielle Methode, mit der aus zwei gegebenen Gruppen eine neue Gruppe konstruiert werden kann. Diese Konstruktion verallgemeinert das Konzept des direkten Produkts von Gruppen und ist selbst ein Spezialfall des Konzepts der Gruppenerweiterung zweier Gruppen.
  • En la teoría de grupos, un producto semidirecto describe una forma particular en la cual un grupo puede ser compuesto de dos subgrupos.
  • En théorie des groupes, le produit semi-direct permet de définir un groupe G à partir de deux groupes H et K, et généralise la notion de produit direct de deux groupes.
  • In algebra, il prodotto semidiretto è un'estensione del concetto di prodotto diretto. Così come il prodotto diretto, un prodotto semidiretto di due gruppi ha sempre come elementi quelli del prodotto cartesiano ; la legge di composizione dipende però anche da un omomorfismo particolare scelto fra gli omomorfismi .
  • 群論において、群の半直積(はんちょくせき、英: semidirect product)とは、ふたつの群から新たな群を作り出す方法の一種。群の直積の一般化であり、通常の直積をその特別な場合として含む。
  • Полупрямое произведение — конструкция в теории групп, позволяющая строить новую группу по двум группам и , и действию группы на группе автоморфизмами. Полупрямое произведение групп и над обычно обозначается .
  • Em matemática, especificamente na área de álgebra abstrata conhecida como teoria dos grupos, um produto semidireto é um meio particular no qual um grupo pode ser colocado junto de dois subgrupos, um dos quais é um subgrupo normal. Um produto semidireto é uma generalização de um produto direto. Um produto semidireto é um produto cartesiano como um conjunto, mas com uma operação multiplicação particular.
  • 在數學中,特別是叫做群論的抽象代數領域中,半直積(semidirect product)是從其中一個是正規子群的兩個子群形成一個群的特定方法。半直積是直積的推廣。半直積是作為集合的笛卡爾積,但帶有特定的乘法運算。
  • In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: an inner semidirect product is a particular way in which a group can be constructed from two subgroups, one of which is a normal subgroup, while an outer semidirect product is a Cartesian product as a set, but with a particular multiplication operation. As with direct products, there is a natural equivalence between inner and outer semidirect products, and both are commonly referred to simply as semidirect products.
sameAs
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
Faceted Search & Find service v1.17_git39 as of Aug 09 2019


Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3232 as of Aug 9 2019, on Linux (x86_64-generic-linux-glibc25), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2019 OpenLink Software