6Symmetric groups II

IA Groups

6 Symmetric groups II

In this chapter, we will look at conjugacy classes of

S

n

and

A

n

. It turns out this

is easy for

S

n

, since two elements are conjugate if and only if they have the same

cycle type. However, it is slightly more complicated in

A

n

. This is since while

(1 2 3) and (1 3 2) might be conjugate in

S

4

, the element needed to perform the

conjugation might be odd and not in A

n

.