Center (group theory)
In abstract algebra, the center of a group, G, is the set of elements that commute with every element of G. It is denoted Z(G), from German Zentrum, meaning center. In set-builder notation, Z(G) = { z ∈ G | ∀g ∈ G, zg = gz}. The center is a normal subgroup, Z(G) ⊲ G. As a subgroup, it is always characteristic, but is not necessarily fully characteristic. The quotient group, G / Z(G), is isomorphic to the inner automorphism group, Inn(G). The elements of the center are sometimes called central.
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Center (group theory)
In abstract algebra, the center of a group, G, is the set of elements that commute with every element of G. It is denoted Z(G), from German Zentrum, meaning center. In set-builder notation, Z(G) = { z ∈ G | ∀g ∈ G, zg = gz}. The center is a normal subgroup, Z(G) ⊲ G. As a subgroup, it is always characteristic, but is not necessarily fully characteristic. The quotient group, G / Z(G), is isomorphic to the inner automorphism group, Inn(G). The elements of the center are sometimes called central.
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Centrum grupy je pojem užívaný ...... h automorfismů jednoprvkovou .
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Centrum, Z(G), även betecknat ...... r isomorf med Kleins fyrgrupp.
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En teoría de grupos, el centro ...... pueden conmutar con el resto.
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En théorie des groupes, on app ...... ommutent avec tous les autres.
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En àlgebra abstracta, el centr ...... abelià si i només si Z(G) = G.
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In abstract algebra, the cente ...... are sometimes called central.
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In de abstracte algebra is het ...... egeven definitie voor groepen.
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In matematica, dato un gruppo ...... ruire il gruppo quoziente G/C.
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Na teoria dos grupos, o centro ...... r que Z(G) é um subgrupo de G.
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В абстрактній алгебрі центром ...... називається групою без центру.
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p/c021250
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title
Centre of a group
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comment
Centrum grupy je pojem užívaný ...... h automorfismů jednoprvkovou .
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Centrum, Z(G), även betecknat ...... l och n ≥ 1, så är Z(G) ≠ {e}.
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En teoría de grupos, el centro ...... ular, del resultado siguiente:
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En théorie des groupes, on app ...... ommutent avec tous les autres.
@fr
En àlgebra abstracta, el centr ...... abelià si i només si Z(G) = G.
@ca
In abstract algebra, the cente ...... are sometimes called central.
@en
In de abstracte algebra is het ...... de inverse , omdat voor alle .
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In matematica, dato un gruppo ...... ruire il gruppo quoziente G/C.
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Na teoria dos grupos, o centro ...... r que Z(G) é um subgrupo de G.
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В абстрактній алгебрі центром ...... називається групою без центру.
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label
Center (group theory)
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Centre d'un groupe
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Centre d'un grup
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Centro de um grupo
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Centro de un grupo
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Centro di un gruppo
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Centrum (groepentheorie)
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Centrum (gruppteori)
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Centrum grupy
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Центр групи
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