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- Generating_set_of_a_group abstract "In abstract algebra, a generating set of a group is a subset such that every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.In other words, if S is a subset of a group G, then <S>, the subgroup generated by S, is the smallest subgroup of G containing every element of S, meaning the intersection over all subgroups containing the elements of S; equivalently, <S> is the subgroup of all elements of G that can be expressed as the finite product of elements in S and their inverses.If G = <S>, then we say S generates G; and the elements in S are called generators or group generators. If S is the empty set, then <S> is the trivial group {e}, since we consider the empty product to be the identity.When there is only a single element x in S, <S> is usually written as <x>. In this case, <x> is the cyclic subgroup of the powers of x, a cyclic group, and we say this group is generated by x. Equivalent to saying an element x generates a group is saying that <x> equals the entire group G. For finite groups, it is also equivalent to saying thatx has order |G|.".
- Generating_set_of_a_group wikiPageID "99945".
- Generating_set_of_a_group wikiPageRevisionID "601470022".
- Generating_set_of_a_group hasPhotoCollection Generating_set_of_a_group.
- Generating_set_of_a_group title "Group generators".
- Generating_set_of_a_group urlname "GroupGenerators".
- Generating_set_of_a_group subject Category:Group_theory.
- Generating_set_of_a_group comment "In abstract algebra, a generating set of a group is a subset such that every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.In other words, if S is a subset of a group G, then <S>, the subgroup generated by S, is the smallest subgroup of G containing every element of S, meaning the intersection over all subgroups containing the elements of S; equivalently, <S> is the subgroup of all elements of G that can be expressed as the finite product of elements in S and their inverses.If G = <S>, then we say S generates G; and the elements in S are called generators or group generators. ".
- Generating_set_of_a_group label "Conjunto generador de un grupo".
- Generating_set_of_a_group label "Conjunto gerador de um grupo".
- Generating_set_of_a_group label "Endlich erzeugte Gruppe".
- Generating_set_of_a_group label "Generating set of a group".
- Generating_set_of_a_group label "Genererende verzameling".
- Generating_set_of_a_group label "Insieme di generatori".
- Generating_set_of_a_group label "Partie génératrice d'un groupe".
- Generating_set_of_a_group label "Zbiór generatorów grupy".
- Generating_set_of_a_group label "Порождающее множество группы".
- Generating_set_of_a_group label "مجموعة مولدة لزمرة".
- Generating_set_of_a_group label "群的生成集合".
- Generating_set_of_a_group sameAs Generování_grupy.
- Generating_set_of_a_group sameAs Endlich_erzeugte_Gruppe.
- Generating_set_of_a_group sameAs Conjunto_generador_de_un_grupo.
- Generating_set_of_a_group sameAs Partie_génératrice_d'un_groupe.
- Generating_set_of_a_group sameAs Insieme_di_generatori.
- Generating_set_of_a_group sameAs Genererende_verzameling.
- Generating_set_of_a_group sameAs Zbiór_generatorów_grupy.
- Generating_set_of_a_group sameAs Conjunto_gerador_de_um_grupo.
- Generating_set_of_a_group sameAs m.0pg_x.
- Generating_set_of_a_group sameAs Q734209.
- Generating_set_of_a_group sameAs Q734209.
- Generating_set_of_a_group wasDerivedFrom Generating_set_of_a_group?oldid=601470022.
- Generating_set_of_a_group isPrimaryTopicOf Generating_set_of_a_group.