Isomorphism of groupsAQA A-Level Further Maths: Mind map

Exam questions on Isomorphism of groups

1. The set $G=\{1,i,-1,-i\}$ under complex multiplication, and the set $H=\{0,1,2,3\}$ under addition modulo 4. The function $\phi:H\to G$ is defined by $\phi(n)=i^n$.
   Verify that $\phi(2+_43)=\phi(2)\times\phi(3)$.2 marks
2. The set $G=\{1,3,5,7\}$ under multiplication modulo 8, and the cyclic group $C_4=\{e,a,a^2,a^3\}$ with $a^4=e$.
   Deduce that $G$ and $C_4$ are not isomorphic.2 marks
3. The set $A=\{0,1,2,3,4,5\}$ under addition modulo 6, and the set $B=\{1,2,3,4,5,6\}$ under multiplication modulo 7.
   Show that $3$ is a generator of $B$.3 marks