Show that the set of numbers \(\{ 3,5,7 \}\), under multiplication modulo 8, does not form a group.
The set of numbers \(\{ 3,5,7 , a \}\), under multiplication modulo 8 , forms a group. Write down the value of \(a\).
State, justifying your answer, whether or not the group in part (ii) is isomorphic to the multiplicative group \(\left\{ e , r , r ^ { 2 } , r ^ { 3 } \right\}\), where \(e\) is the identity and \(r ^ { 4 } = e\).