Difference between revisions of "Commutator subgroup"
From Maths
(Created page with "==Definition== Let {{M|C}} be the group generated by the set of all commutators of a group {{M|(G,\times)}}. Then {{M|C}} is a S...") |
m |
||
| Line 1: | Line 1: | ||
==Definition== | ==Definition== | ||
| − | 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 C be the group generated by the set of all commutators of a group (G,×). Then C is a sugroup of G, furthermore it is a normal subgroup. That is to say:
- C=⟨{[g,h]∈G | g,h∈G}⟩
TODO: Finish page
