Group isomorphic to its automorphism group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Relation with other properties
- A nontrivial group of prime power order cannot be a complete group, because a group of prime power order is either of prime order or has outer automorphism class of same prime order. However, it may still be isomorphic to its automorphism group. The only known example so far is dihedral group:D8. Whether there exist other groups isomorphic to their automorphism groups is an open problem.