(7 marks) Recall that S4 is the group consisting of the set of all bijections from {1,2,3,4} to {1,2,3,4} together with the binary operation ◦ denoting composition of functions. You may use arrow diagrams to represent bijections of S4 and perform compositions of bijections.
AIs S4 abelian? Justify your answer.
BDetermine the cyclic subgroup ⟨f⟩ of S4, where f ∈ S4 is the bijection defined by f(1) = 3, f(2) = 4, f(3) = 1, f(4) =2.
CDetermine a cyclic subgroup of S4 that is isomorphic to (Z4,+), and give an isomorphism between these two groups.
AIs S4 abelian? Justify your answer.
BDetermine the cyclic subgroup ⟨f⟩ of S4, where f ∈ S4 is the bijection defined by f(1) = 3, f(2) = 4, f(3) = 1, f(4) =2.
CDetermine a cyclic subgroup of S4 that is isomorphic to (Z4,+), and give an isomorphism between these two groups.