Generalization of Cauchy's Equation

[square173205]

Cauchy's equation is expressed as,

 

f(x+y) = f(x)+f(y)

 

In the following site:

http://hecoaustralia.fortunecity.com/cauchy/cauchyequation.htm

I tried to expand the Cauchy's equation to general group homomorphism.

[square173205]

Commutator group has a close relationship with abelian extension of field. However if the extension of the field is not abelian, we would need the other group to form the solvable group. In the following site I tried to generalize the commutator group for that purpose.

 

http://hecoaustralia.fortunecity.com/commutator/algebra.htm

[Dave]

Would appreciate it if you shared some of these ideas on the forum instead of linking to ad-riddled pages!