- A binary operation * is defined on positive real numbers by
$$a * b = a + b + a b$$
Prove that the operation * is associative.
(ii) The set \(G = \{ 1,2,3,4,5,6 \}\) forms a group under the operation of multiplication modulo 7
- Show that \(G\) is cyclic.
The set \(H = \{ 1,5,7,11,13,17 \}\) forms a group under the operation of multiplication modulo 18
- List all the subgroups of \(H\).
- Describe an isomorphism between \(G\) and \(H\).