P-extensible implies inner

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 $\sigma$ is an automorphism of $P$ such that for any $p$-group $Q$ containing $P$, there is an automorphism ${\sigma }^{\prime }$ of $Q$ whose restriction to $P$ equals $\sigma$. Then, $\sigma$ 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 copyMore info}