P-extensible implies inner

From Groupprops

Statement

Suppose $p$ is a prime number and $P$ is a p-group, i.e., a group in which the order of every element is a power of $p$ . Suppose $σ$ is an automorphism of $P$ such that for any $p$ -group $Q$ containing $P$ , there is an automorphism $σ'$ of $Q$ whose restriction to $P$ equals $σ$ . Then, $σ$ is an inner automorphism of $P$ .

References

Journal references

Characterizing inner automorphisms of groups by Martin R. Pettet, Archiv der Mathematik, ISSN 1420-8938 (Online), ISSN 0003-889X (Print), Volume 55,Number 5, Page 422 - 428(Year 1990): ^{Springerlink official copy}^{More info}