Suppose h:D12->z/12z is a homomorphism of groups.Prove that g(t^2)=[0] mod 12

My attempt so far is

g(t6) = [0]9

by Homomorphism

g(a*b)=g(a) * g(b)

g(t^2*t^2*t^2) = g(t2) *g(t2)*g(t2)

g(t6)

0 = 3g(t2)

- May 1st 2008, 03:11 PMgoldstarSuppose h:D12->z/12z is a homomorphism of groups.Prove that g(t^2)=[0] mod 12
Suppose h:D12->z/12z is a homomorphism of groups.Prove that g(t^2)=[0] mod 12

My attempt so far is

g(t6) = [0]9

by Homomorphism

g(a*b)=g(a) * g(b)

g(t^2*t^2*t^2) = g(t2) *g(t2)*g(t2)

g(t6)

0 = 3g(t2)