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}.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Showing that a certain subgroup is the kernal of a homomorphism

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