 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2014/prelims/mathematics-i/6/a/i/solution

N

G

is a normal subgroup if conjugation by every element preserves it:

g N g^{- 1} = N for every g \in G .

Equivalently,

g N = N g

for every

g \in G

. Here equality means equality of sets; it does not require each individual element of

N

to commute with every element of

G

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