Find a homomorphism from the quaternion group $Q$ onto $\mathbb{Z}_8^\ast$.
Hint: The kernel must be a normal subgroup of order 2, use the multiplication table of $Q$. Ans: $\Phi(\pm 1) = 1, \Phi(\pm i) = 3, \Phi(\pm j)= 5, \Phi(\pm k)=7$. The 3,5 and 7 can be permuted. ^ for this question, the answer is given as you can see, I just need to understand it step by step. Thank you
P.S: Multiplication table of $Q$ is:Multiplication Table of Q
