An improved characterisation of inner automorphisms of groups
Group Theory
2026-05-11 v2
Abstract
We show that every group embeds malnormally into a simple, complete co-Hopfian group . This implies that a non-trivial endomorphism of extends to if and only if it is an inner automorphism, strengthening a theorem of Schupp and answering a question of Bergman.
Keywords
Cite
@article{arxiv.2604.05728,
title = {An improved characterisation of inner automorphisms of groups},
author = {Francesco Fournier-Facio},
journal= {arXiv preprint arXiv:2604.05728},
year = {2026}
}
Comments
7 pages. v2: small changes