GroupsAQA A-Level Further Maths: Mind map

Exam questions on Groups

1. The set $G=\{1,5,7,11\}$ under multiplication modulo 12.
   Determine whether $G$ is cyclic, justifying your answer.2 marks
2. The set $T$ of symmetries of an equilateral triangle forms a group under composition: the identity, rotations through $120^\circ$ and $240^\circ$ about the centre, and reflections in the three lines of symmetry.
   Explain why $T$ is not abelian.2 marks
3. The set $G=\{0,1,2,3,4,5\}$ under addition modulo 6, written $+_6$.
   Given that $G$ is closed under $+_6$, show that $(G,+_6)$ satisfies the other three group axioms.3 marks