How many elements of order 2 does the symmetric group S4 con

How many elements of order 2 does the symmetric group S4 contain?

Solution

There are 4! = 24 elements in S₄. The elements are all such permutations of {1,2,3,4}.

Let S 4.

Then =(a₁a₂) and ( a₁a₂)² order 2

Thus, the elements of order 2 that the symmetric group S4 contain are listed below:

(1 2),(1 3),(1 4),(2 3),(2 4),(3 4),(1 2)(3 4),(1 3)(2 4),(1 4)(2 3).

Thus, there are 9 elements of order 2.