Let G = (Z/8Z)x = {[x] | gcd(x, 8) = 1}, and let · be the operation on G given by [x]·[y] = [x·y]. 1. List the elements of G. 2. Construct the Cayley table for G. 3. Determine whether G has an identity, and if so give it. 4. For each element of G, find its inverse. 5. For each element of G, find its order.
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Let G = (Z/8Z)x = {[x] | gcd(x, 8) = 1}, and let · be the operation on G given by [x]·[y] = [x·y].
1. List the elements of G.
2. Construct the Cayley table for G.
3. Determine whether G has an identity, and if so give it.
4. For each element of G, find its inverse.
5. For each element of G, find its order.
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