Difference between revisions of "Commutator subgroup"
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| − | Let {{M|C}} be the group [[Generated | + | Let {{M|C}} be the group [[Generated subgroup|generated]] by the set of all [[Commutator|commutators]] of a [[Group|group]] {{M|(G,\times)}}. Then {{M|C}} is a [[Subgroup|sugroup]] of {{M|G}}, furthermore it is a [[Normal subgroup|normal subgroup]]. That is to say: |
* <math>C=\langle\{[g,h]\in G\ |\ g,h\in G\}\rangle</math> | * <math>C=\langle\{[g,h]\in G\ |\ g,h\in G\}\rangle</math> | ||
Latest revision as of 11:21, 12 May 2015
Definition
Let [ilmath]C[/ilmath] be the group generated by the set of all commutators of a group [ilmath](G,\times)[/ilmath]. Then [ilmath]C[/ilmath] is a sugroup of [ilmath]G[/ilmath], furthermore it is a normal subgroup. That is to say:
- [math]C=\langle\{[g,h]\in G\ |\ g,h\in G\}\rangle[/math]
TODO: Finish page
