Consider the following groups G and H,K G. If G is isomorphic to H K, give...

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Consider the following groups G and H,K G. If G is isomorphic to H K, give an isomorphism 4 : G H K. If not, say why G and H K cannot be isomorphic. (a) GR, H = {1, 1}, K = R+ (b) G = D4, H = {1,r,r, r}, K = {1, s} Consider the following groups G and H,K G. If G is isomorphic to H K, give an isomorphism 4 : G H K. If not, say why G and H K cannot be isomorphic. (a) GR, H = {1, 1}, K = R+ (b) G = D4, H = {1,r,r, r}, K = {1, s}

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a For the groups G R H 1 1 and K R we can show that G is isomorphic to H x K Define the f... View the full answer