- #1
demonelite123
- 219
- 0
Let Q be the quaternion group {1, -1, i, -i, j, -j, k, -k}. Show that the normal subgroup {1, -1, i, -i} is the kernal of a homomorphism from Q to {1, -1}.
I know that if N is a normal subgroup of G then the homomorphism f: G -> G/N has N as the kernal of f. while i can get the kernal of f to be {1, -1, i, -i} i can't seem to get the codomain to be {1, -1}. I've gone through different mappings and all of them while they had the correct kernal always seem to have more than just {1, -1} in the codomain. can someone help me determine the correct homomorphism?
I know that if N is a normal subgroup of G then the homomorphism f: G -> G/N has N as the kernal of f. while i can get the kernal of f to be {1, -1, i, -i} i can't seem to get the codomain to be {1, -1}. I've gone through different mappings and all of them while they had the correct kernal always seem to have more than just {1, -1} in the codomain. can someone help me determine the correct homomorphism?