Prime-extensible automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |

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Definition

Let $p$ be a prime. An automorphism of a group whose order is a power of $p$ is said to be $p$-extensible if for any embedding of the group in a bigger goup whose order is a power of the same prime, the automorphism can be extended to an automorphism of the bigger group.

Relation with other properties

Weaker properties

• Finite-extensible automorphism (for a group of prime power order)

Related properties

• Prime set-extensible automorphism