## Question

###### Determine whether O not the group G = {L,i,-1,~i} (with i=V-1 under multiplication is isomorphic to the group U(8) = {1,3,5,7} with multiplication mod &. If the groups are not isomorphic, give a clear reason, justifying your statements If the groups are isomorphic, define a map from one to the other and prove it is an isomorphism: The Cayley table for U(8) is given to save time computing: You do not need to prove G is & group. (10 points) 3 5 7 3 5 3 5 5 5 7 3 7 7 |5 | 3 1

Determine whether O not the group G = {L,i,-1,~i} (with i=V-1 under multiplication is isomorphic to the group U(8) = {1,3,5,7} with multiplication mod &. If the groups are not isomorphic, give a clear reason, justifying your statements If the groups are isomorphic, define a map from one to the other and prove it is an isomorphism: The Cayley table for U(8) is given to save time computing: You do not need to prove G is & group. (10 points) 3 5 7 3 5 3 5 5 5 7 3 7 7 |5 | 3 1

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