Metabelian group
In mathematics, a metabelian group is a group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there is an abelian normal subgroup A such that the quotient group G/A is abelian. Subgroups of metabelian groups are metabelian, as are images of metabelian groups over group homomorphisms. Metabelian groups are solvable. In fact, they are precisely the solvable groups of derived length at most 2.
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Metabelian group
In mathematics, a metabelian group is a group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there is an abelian normal subgroup A such that the quotient group G/A is abelian. Subgroups of metabelian groups are metabelian, as are images of metabelian groups over group homomorphisms. Metabelian groups are solvable. In fact, they are precisely the solvable groups of derived length at most 2.
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Em matemática, um grupo metabe ...... rupo quociente G/A é abeliano.
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Im mathematischen Gebiet der G ...... scher Gruppen zerlegen lassen.
@de
In mathematics, a metabelian g ...... s of derived length at most 2.
@en
Inom matematiken är en metabel ...... att kvotgruppen G/A är abelsk.
@sv
群論中,亞阿貝爾群是指其換位子群是阿貝爾群的一種群,也就是說 ...... 都是亞阿貝爾群。 亞阿貝爾群正是其導出列長不大於2的可解群。
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Em matemática, um grupo metabe ...... rupo quociente G/A é abeliano.
@pt
Im mathematischen Gebiet der G ...... scher Gruppen zerlegen lassen.
@de
In mathematics, a metabelian g ...... s of derived length at most 2.
@en
Inom matematiken är en metabel ...... att kvotgruppen G/A är abelsk.
@sv
群論中,亞阿貝爾群是指其換位子群是阿貝爾群的一種群,也就是說 ...... 都是亞阿貝爾群。 亞阿貝爾群正是其導出列長不大於2的可解群。
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Grupo metabeliano
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Metabelian group
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Metabelsche Gruppe
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Metabelsk grupp
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亞阿貝爾群
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