Question

Give an example of non abelian group consisting of 8 elements

Answer 1

Answer:

•♠♦A very simple example: let G be the group of permutations of Z. Denote by s the ‘symmetry’ x↦-x and t be the ‘translation’ x↦x+1. s is of order 2, but t has infinite order – indeed, t^k is simply x↦x+k. Now, it's easy to check s o t has order 2 like s, but s o(s o t)=t has infinite order.♠♦•