# Prime set-extensible automorphism

From Groupprops

Template:Prime set-parametrized automorphism property

This is a variation of extensible automorphism|Find other variations of extensible automorphism |

This term is related to: Extensible automorphisms problem

View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Definition with symbols

Let be a set of primes. Let be a -group, viz a finite group such that all prime divisors of its order are in . An automorphism of is said to be -extensible if it can be extended to an automorphism of for any -group containing .

## Relation with other properties

### Particular cases

- Prime-extensible automorphism: A particular case when the prime set is a singleton set
- Finite-extensible automorphism: A particular case when the prime set is the set of all primes