Free product
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a homomorphism from G ∗ H to K. Unless one of the groups G and H is trivial, the free product is always infinite. The construction of a free product is similar in spirit to the construction of a free group (the universal group with a given set of generators).
Wikipage disambiguates
Adian–Rabin theoremAdjoint functorsAlgebraically closed groupAmalgamated groupAmalgamated productAmalgamationAmalgamation propertyArtin–Tits groupAsteriskBass–Serre theoryBiproductBrian BowditchBrunnian linkCategory of groupsCategory of ringsCoproductCumulantDatabase marketingDirect productDirect sumDirect sum of groupsEgyptian fractionEnd (graph theory)EpimorphismFree groupFree independenceFree probabilityFree product of associative algebrasFree product of groupsFree product with amalgamated subgroupFree product with amalgamationFree products with amalgamationFreiheitssatzFundamental groupGeometric group theoryGlossary of category theoryGraph of groupsGroup cohomologyGrushko theoremHNN extension
Link from a Wikipage to another Wikipage
seeAlso
primaryTopic
Free product
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a homomorphism from G ∗ H to K. Unless one of the groups G and H is trivial, the free product is always infinite. The construction of a free product is similar in spirit to the construction of a free group (the universal group with a given set of generators).
has abstract
En las matemáticas, particular ...... lejo es que se interpreta como
@es
En mathématiques, et plus part ...... libre est le groupe libre FI.
@fr
In algebra, il prodotto libero ...... spazi topologici per un punto.
@it
In mathematics, specifically g ...... ver a cyclic group of order 2.
@en
Свободным произведением групп ...... едение и обычно обозначается .
@ru
У теорії груп вільним добутком ...... груп і алгебричній топології.
@uk
在數學的群論中，自由積（英語：free product，法語 ...... 成元集合所能構造出的最一般的群）相似。 自由積是群範疇中的。
@zh
数学、とくに群論における自由積（じゆうせき、英: free ...... 交和の普遍群はそれら群の自由積（＝余積）に一致するのである。
@ja
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,020,377,253
Link from a Wikipage to another Wikipage
title
Free product with amalgamated subgroup
@en
Free product
@en
wikiPageUsesTemplate
comment
En las matemáticas, particular ...... grupos G y H respectivamente.
@es
En mathématiques, et plus part ...... d'un morphisme de G∗H dans K.
@fr
In algebra, il prodotto libero ...... spazi topologici per un punto.
@it
In mathematics, specifically g ...... th a given set of generators).
@en
Свободным произведением групп ...... едение и обычно обозначается .
@ru
У теорії груп вільним добутком ...... груп і алгебричній топології.
@uk
在數學的群論中，自由積（英語：free product，法語 ...... 成元集合所能構造出的最一般的群）相似。 自由積是群範疇中的。
@zh
数学、とくに群論における自由積（じゆうせき、英: free ...... せて得られる空間）の基本群は単に空間の基本群の自由積である。
@ja
label
Free product
@en
Freies Produkt
@de
Prodotto libero
@it
Producto libre de grupos
@es
Produit libre
@fr
Вільний добуток
@uk
Свободное произведение
@ru
自由積
@ja
自由積
@zh
자유곱
@ko