Inner implies extensible
This article gives the statement and possibly, proof, of an implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., inner automorphism) must also satisfy the second automorphism property (i.e., extensible automorphism)
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Statement with symbols
Let be groups and an inner automorphism of , there is an automorphism of such that the restriction of is .
The proof in fact follows from the result:
and the fact that every inner automorphism is an automorphism.