 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/9/b/solution

g

Cl_{G} (g) = {h g h^{- 1} : h \in G} .

N

g \in N

, then normality gives

h g h^{- 1} \in N

for every

h

. Thus the whole conjugacy class of each member of

N

is contained in

N

, and

N = g \in N ⋃ Cl_{G} (g) .

Conjugacy classes partition the group, so this is a union of complete disjoint classes, never selected fractions of classes.

 New to topics? Read the docs here!