Publikationsdetails
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
- Organisationseinheit(en)
-
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Typ
- Artikel
- Journal
- Advances in Group Theory and Applications
- Band
- 22
- Seiten
- 155–175
- Anzahl der Seiten
- 21
- ISSN
- 2499-1287
- Publikationsdatum
- 12.2025
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Algebra und Zahlentheorie
- Elektronische Version(en)
-
https://doi.org/10.32037/agta-2025-018 (Zugang:
Offen
)
https://doi.org/10.48550/arXiv.2405.02992 (Zugang: Offen )
