I need help on this question!
Suppose G is an Abelian Group and let f:G--> G be the function defined by f(x)=x^3
i) show that f is a group homomorphism
ii) show that f is an group homomorphism iff lGl is not divisible by 3
I need help on this question!
Suppose G is an Abelian Group and let f:G--> G be the function defined by f(x)=x^3
i) show that f is a group homomorphism
ii) show that f is an group homomorphism iff lGl is not divisible by 3
thankyou for your help..the 1st part is pretty straight forward, however I did make a mistake with the second part it states
ii) show that f is an isomorphism iff lGl is not divisible by 3.
I don't quite understand how showing a^3=1 => a=1 shows that lGl is not divisible by 3.