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- Free_group abstract "In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st = suu−1t, but s ≠ t for s,t,u∈S). The members of S are called generators of FS.An arbitrary group G is called free if it is isomorphic to FS for some subset S of G, that is, if there is a subset S of G such that every element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st = suu−1t).A related but different notion is a free abelian group, both notions are particular instances of a free object from universal algebra.".
- Free_group thumbnail F2_Cayley_Graph.png?width=300.
- Free_group wikiPageExternalLink books?id=LJtyhu8-xYwC&pg=PA27.
- Free_group wikiPageExternalLink books?id=deWkZWYbyHQC&pg=PA70.
- Free_group wikiPageID "59735".
- Free_group wikiPageRevisionID "595607227".
- Free_group hasPhotoCollection Free_group.
- Free_group subject Category:Articles_with_inconsistent_citation_formats.
- Free_group subject Category:Combinatorial_group_theory.
- Free_group subject Category:Free_algebraic_structures.
- Free_group subject Category:Geometric_group_theory.
- Free_group subject Category:Group_theory.
- Free_group subject Category:Properties_of_groups.
- Free_group type Artifact100021939.
- Free_group type FreeAlgebraicStructures.
- Free_group type Object100002684.
- Free_group type PhysicalEntity100001930.
- Free_group type Structure104341686.
- Free_group type Whole100003553.
- Free_group type YagoGeoEntity.
- Free_group type YagoPermanentlyLocatedEntity.
- Free_group comment "In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st = suu−1t, but s ≠ t for s,t,u∈S).".
- Free_group label "Free group".
- Free_group label "Freie Gruppe".
- Free_group label "Groupe libre".
- Free_group label "Grupa wolna".
- Free_group label "Grupo libre".
- Free_group label "Grupo livre".
- Free_group label "Gruppo libero".
- Free_group label "Vrije groep".
- Free_group label "Свободная группа".
- Free_group label "自由群".
- Free_group label "自由群".
- Free_group sameAs Freie_Gruppe.
- Free_group sameAs Grupo_libre.
- Free_group sameAs Groupe_libre.
- Free_group sameAs Gruppo_libero.
- Free_group sameAs 自由群.
- Free_group sameAs Vrije_groep.
- Free_group sameAs Grupa_wolna.
- Free_group sameAs Grupo_livre.
- Free_group sameAs m.0g860.
- Free_group sameAs Q431078.
- Free_group sameAs Q431078.
- Free_group sameAs Free_group.
- Free_group wasDerivedFrom Free_group?oldid=595607227.
- Free_group depiction F2_Cayley_Graph.png.
- Free_group isPrimaryTopicOf Free_group.