# Prime set-extensible automorphism

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

## Contents

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

## Definition

### Definition with symbols

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