Publication details
Characterizing inner automorphisms and realizing outer automorphisms
Abstract
We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite group, whose outer automorphism group is isomorphic to G. The first theorem was proved by Pettet using a graph-theoretical construction given by Heineken–Liebeck. A Lie-theoretical proof of the second theorem was sketched by Cornulier in a MathOverflow post. Our proofs are purely group-theoretical.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Advances in Group Theory and Applications
- Volume
- 22
- Pages
- 155–175
- No. of pages
- 21
- ISSN
- 2499-1287
- Publication date
- 12.2025
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Algebra and Number Theory
- Electronic version(s)
-
https://doi.org/10.32037/agta-2025-018 (Access:
Open
)
https://doi.org/10.48550/arXiv.2405.02992 (Access: Open )
