English

The finite groups with three automorphism orbits

Group Theory 2025-05-07 v2

Abstract

A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem initiated by G. Higman in 1963. As a consequence, a classification is obtained for finite permutation groups of rank 33 which are holomorphs of groups.

Keywords

Cite

@article{arxiv.2403.01725,
  title  = {The finite groups with three automorphism orbits},
  author = {Cai Heng Li and Yan Zhou Zhu},
  journal= {arXiv preprint arXiv:2403.01725},
  year   = {2025}
}

Comments

22 pages

R2 v1 2026-06-28T15:07:53.591Z