Recall that a subgroup N of a group G is called characteristic if F(N)=N for all automorphisms F of G. If N is a characteristic subroup of G, show that N is a normal subgroup of G.
I don't have a clue were to start this from, any help would be great
Recall that a subgroup N of a group G is called characteristic if F(N)=N for all automorphisms F of G. If N is a characteristic subroup of G, show that N is a normal subgroup of G.
I don't have a clue were to start this from, any help would be great
If F(N)=N for all automorphisms F of G, then for every inner automorphism .
Now for every implies that for every . It follows that N is a normal subgroup of G.