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
.