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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- May 9th 2010, 07:44 PMtas10homomorphism
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 - May 9th 2010, 07:46 PMDrexel28