Groupprops, The Group Properties Wiki (pre-alpha)

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 copyMore info}