Explore BrainMass
Share

Explore BrainMass

    Projection homomorphism: normal subgroup

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let M be a normal subgroup of a group G and let N be a normal subgroup of a group H. Use the first Isomorphism Theorem to prove that M X N is normal subgroup of G X H and that (G X H) / (M X N) is isomorphic to G/M X H/N

    © BrainMass Inc. brainmass.com October 10, 2019, 2:24 am ad1c9bdddf
    https://brainmass.com/math/linear-transformation/projection-homomorphism-normal-subgroup-375620

    Solution Preview

    Since M is a normal subgroup of G, there's the projection homomorphism p: G -> G/M given by p(g) = gM, and M=ker(p).
    Since N is normal in H, there's the projective homomorphism q: H -> H/N given by q(h) = hN, and N = ker(q).

    Define a map s: G X H -> G/M ...

    Solution Summary

    This solution clearly assesses the projection homomorphism.

    $2.19