# Prime-extensible automorphism

From Groupprops

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 be a prime. An automorphism of a group whose order is a power of is said to be -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.