English

An improved characterisation of inner automorphisms of groups

Group Theory 2026-05-11 v2

Abstract

We show that every group GG embeds malnormally into a simple, complete co-Hopfian group HH. This implies that a non-trivial endomorphism of GG extends to HH 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