Extensible automorphism-invariant equals normal
This article gives a proof/explanation of the equivalence of multiple definitions for the term normal subgroup
View a complete list of pages giving proofs of equivalence of definitions
The following are equivalent for a subgroup of a group:
- The subgroup is a normal subgroup: it is invariant under all inner automorphisms of the whole group.
- The subgroup is an extensible automorphism-invariant subgroup: it is invariant under all extensible automorphisms of the whole group.