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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 thatf(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?
Let epsilon, gamma >0. If x is epsilon-close to y, and y is gamma-close to z, then x and z are (epsilon + gamma)-close. Let epsilon>0. If y and z are both epsilon close to x, and w is between y and z (i.e.. y
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