G = Z_4 x Z_4 prove that the map theta: Z_4 x Z_4 --> Z_4 defined by theta(([a],[b])) = [b] is a homomorphism ONTO Z_4. what is the kernel of theta? Show that the quotient group G/<([1],[0])> is isomorphic to Z_4
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Originally Posted by tas10 G = Z_4 x Z_4 prove that the map theta: Z_4 x Z_4 --> Z_4 defined by theta(([a],[b])) = [b] is a homomorphism ONTO Z_4. what is the kernel of theta? Show that the quotient group G/<([1],[0])> is isomorphic to Z_4 Where's the work? It's just as easy to prove in general the projection $\displaystyle \pi:G\times H\to Gg,h)\mapsto g$ is an epimorphism.
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