the derived subgroup is normal
We have to show that for each , it is also in .
Since is the subgroup generated by the all commutators in , then for each we have –a word of commutators– so for all .
Now taking any element of we can see that
so a conjugation of a commutator is another commutator, then for the conjugation
is another word of commutators, hence is in which in turn implies that is normal in , QED.
|Title||the derived subgroup is normal|
|Date of creation||2013-03-22 16:04:39|
|Last modified on||2013-03-22 16:04:39|
|Last modified by||juanman (12619)|