About: Baumslag–Solitar group

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In the mathematical field of group theory, the Baumslag–Solitar groups are examples of two-generator one-relator groups that play an important role in combinatorial group theory and geometric group theory as (counter)examples and test-cases. They are given by the group presentation For each integer m and n, the Baumslag–Solitar group is denoted BS(m, n). The relation in the presentation is called the Baumslag–Solitar relation. Some of the various BS(m, n) are well-known groups. BS(1, 1) is the free abelian group on two generators, and BS(1, −1) is the fundamental group of the Klein bottle.

Attributes	Values
rdfs:label	Baumslag–Solitar group (en) Groupe de Baumslag-Solitar (fr) Группа Баумслага — Солитера (ru) Група Баумслага — Солітера (uk)
rdfs:comment	En mathématiques et notamment en théorie des groupes, les groupes de Baumslag-Solitar sont des exemples de groupes à deux générateurs et un relateur qui jouent un rôle important dans la théorie combinatoire des groupes et en théorie géométrique des groupes comme exemples ou contre-exemples. (fr) Група Баумслага — Солітера — група з двома твірними і і одним співвідношенням Зазвичай, цю групу позначають . (uk) Группа Баумслага — Солитера — группа с двумя образующими и и одним соотношением Обычно, эта группа обычно обозначается . (ru) In the mathematical field of group theory, the Baumslag–Solitar groups are examples of two-generator one-relator groups that play an important role in combinatorial group theory and geometric group theory as (counter)examples and test-cases. They are given by the group presentation For each integer m and n, the Baumslag–Solitar group is denoted BS(m, n). The relation in the presentation is called the Baumslag–Solitar relation. Some of the various BS(m, n) are well-known groups. BS(1, 1) is the free abelian group on two generators, and BS(1, −1) is the fundamental group of the Klein bottle. (en)
foaf:depiction
dcterms:subject	Combinatorial group theory
Wikipage page ID	11485892 (xsd:integer)
Wikipage revision ID	1026392287 (xsd:integer)
Link from a Wikipage to another Wikipage	Donald Solitar Anatoly Maltsev Mathematics Geometric group theory Generating set of a group Combinatorial group theory Fundamental group Hopfian group Linear group Combinatorial group theory Binary tiling Bulletin of the AMS Free abelian group Group theory Klein bottle Gilbert Baumslag Residually finite Group presentation
sameAs	Baumslag–Solitar group Baumslag–Solitar group Baumslag–Solitar group Baumslag–Solitar group Baumslag–Solitar group Baumslag–Solitar group Baumslag–Solitar group
dbp:wikiPageUsesTemplate	dbt:Springer dbt:! dbt:= dbt:Math dbt:MR
thumbnail	wiki-commons:Special:FilePath/Baumslag-Solitar_Cayley.svg?width=300
author	D.J. Collins (en)
id	B/b130070 (en)
title	Baumslag–Solitar group (en)
has abstract	In the mathematical field of group theory, the Baumslag–Solitar groups are examples of two-generator one-relator groups that play an important role in combinatorial group theory and geometric group theory as (counter)examples and test-cases. They are given by the group presentation For each integer m and n, the Baumslag–Solitar group is denoted BS(m, n). The relation in the presentation is called the Baumslag–Solitar relation. Some of the various BS(m, n) are well-known groups. BS(1, 1) is the free abelian group on two generators, and BS(1, −1) is the fundamental group of the Klein bottle. The groups were defined by Gilbert Baumslag and Donald Solitar in 1962 to provide examples of non-Hopfian groups. The groups contain residually finite groups, Hopfian groups that are not residually finite, and non-Hopfian groups. (en) En mathématiques et notamment en théorie des groupes, les groupes de Baumslag-Solitar sont des exemples de groupes à deux générateurs et un relateur qui jouent un rôle important dans la théorie combinatoire des groupes et en théorie géométrique des groupes comme exemples ou contre-exemples. (fr) Група Баумслага — Солітера — група з двома твірними і і одним співвідношенням Зазвичай, цю групу позначають . (uk) Группа Баумслага — Солитера — группа с двумя образующими и и одним соотношением Обычно, эта группа обычно обозначается . (ru)
prov:wasDerivedFrom	wikipedia-en:Baumslag–Solitar_group?oldid=1026392287&ns=0
page length (characters) of wiki page	3373 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Baumslag–Solitar_group
is Link from a Wikipage to another Wikipage of	Presentation of a group Hyperbolic group Donald Solitar Geometric group theory Baumslag–Gersten group Subgroup distortion Hopfian group Acylindrically hyperbolic group List of Brooklyn College alumni Schur multiplier Baumslag-Solitar group Baumslag-solitar group Baumslag group Residually finite group Binary tiling Co-Hopfian group Automatic group Howson property One-relator group Gilbert Baumslag
is Wikipage redirect of	Baumslag-Solitar group Baumslag-solitar group
is foaf:primaryTopic of	wikipedia-en:Baumslag–Solitar_group

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