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* [[Every automorphism is center-fixing and inner automorphism group is maximal in automorphism group implies every automorphism is normal-extensible]]

* [[Centerless and ~~inner automorphism group is ~~maximal in automorphism group implies every automorphism is normal-extensible]]

==Examples==

[[Every finite cyclic group occurs as the outer automorphism group of a finite simple non-abelian group]]. More specifically, the cyclic group of order <math>r</math> is the outer automorphism group of the [[projective special linear group of degree two]] <math>PSL(2,2^r)</math>. In particular, when <math>r = p^k</math> for some [[prime number]] <math>p</math> and <math>k \ge 1</math>, we obtain situations where the theorem applies.

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