1 The set \(G = \{ 1,4,5,6,7,9,11,16,17 \}\) is a group of order 9 under the binary operation of multiplication modulo 19.
- Show that \(G\) is a cyclic group generated by the element 4 .
- Find another generator for \(G\). Justify your answer.
- Specify two distinct isomorphisms from the group \(J = \{ 0,1,2,3,4,5,6,7,8 \}\) under addition modulo 9 to \(G\).