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
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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 $G$.

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