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Abelian group

334 bytes added, 16:15, 24 June 2009
Facts
===Occurrence as quotients===
The maximal abelian quotient of any group is termed its [[abelianization]], and this is the quotient by the [[commutator subgroup]]. A subgroup is an [[abelian-quotient subgroup]] (i.e., normal with abelian quotient group ) if and only if the subgroup contains the commutator subgroup. ==Formalisms== {{obtainedbyapplyingthe|diagonal-in-square operator|normal subgroup}} A group <math>G</math> is an abelian group if and only if, in the [[external direct product]] <math>G \times G</math>, the diagonal subgroup <math>\{ (g,g) \mid g \in G \}</math> is a [[normal subgroup]].
==Metaproperties==
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