# Homework Help: Need help!

1. Aug 30, 2010

### tasha10

got it thanks!

Last edited: Aug 30, 2010
2. Aug 30, 2010

### annoymage

homormophism. f(ab)=f(a)f(b) for all a,b in G

so, imagine the domain and codomain, a will maps to f(a), b will map to f(b), so ab must map to f(ab)
so it is homorphism if f(ab)=f(a)f(b)

3. Aug 30, 2010

### tasha10

so, how does this relate to it being commutative? can we say that f(a)f(b)=f(b)f(a)?

4. Aug 30, 2010

### annoymage

that is if and only if proof, so first assume it is homomorphism, so you know f(ab)=f(a)f(b)
so you want to prove f(a)f(b)=f(b)f(a) or ab=ba, prove either one since both domain and codomain are G

and conversely, assume that G is commutative, so you know ab=ba or f(a)f(b)=f(b)f(a) chose either one, to prove that f(ab)=f(a)f(b)