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Groups and proofs

Let A, B, and C be groups, let alpha, beta, and gamma be homomorphisms with gamma times alpha = beta

alpha gamma beta

If alpha is surjective, prove that ker(gamma)= alpha((ker(beta)).

Prove that if K is a subgroup of a group G, and if every left coset of aK is equal to the right coset Kb, then K is a normal subgroup of G.

I just dont know how to do these, the confuse me and I am horrible at writing them in good proof form

Solution Summary

This contains proofs regarding a surjective homomorphism and a normal subgroup.