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Homework answers / question archive / Show that all automorphisms of a group G form a group under function composition
Show that all automorphisms of a group G form a group under function composition.
Then show that the inner automorphisms of G, defined by f : G--->G so that
f(x) = (a^(-1))(x)(a), form a normal subgroup of the group of all automorphisms.
For the first part, I can see that we need to show that f(g(x)) = g(f(x)) for x in G and
use f(x)=x as the identity in the group, but I' not certain how to proceed to show all innG
form a normal subgroup?
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