Central factor-extensible automorphism
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |
An automorphism of a group is termed central factor-extensible if, for every embedding of the group as a central factor of a group, the automorphism can be extended to an automorphism of the bigger group.
Definition with symbols
Relation with other properties
- Extensible automorphism
- Normal-extensible automorphism
- Center-fixing automorphism: For full proof, refer: Center-fixing implies central factor-extensible
In a centerless group, every automorphism is central factor-extensible. This is because any central factor that is centerless as a group must be a direct factor.
Further information: Centerless implies every automorphism is central factor-extensible