Hong Yi Huang


My main interest of research is in group theory, mostly finite groups. I have a particular interest in permutation groups, as well as some related structures in combinatorics (e.g. transitive graphs). I'm also interested in finite simple groups, especially their subgroup structures and conjugacy classes.

More specifically, I mainly work on base sizes (the minimal size of a base) of finite permutation groups. This has been studied since 19th century when permutation group theory was still young, finding a wide range of connections to other areas.

In my recent paper, I determine the precise base size of every finite primitive permutation group of diagonal type. In view of the O'Nan-Scott theorem (5-type version), this is the first family of primitive groups for which people have a complete answer on base sizes.

In 2022, I participated in the Simple groups, representations and applications programme at the Isaac Newton Institute in Cambridge. A brief description of my research on base-two primitive groups and their Saxl graphs up to that time can be found in my poster for this programme.

My Erdős number is 3. For example, there are two disjoint geodesics:

Articles and preprints

  1. On valency problems of Saxl graphs
    joint with J. Chen
    Journal of Group Theory 25 (2022), 543-577.
    arXiv: 2012.13747 | doi: 10.1515/jgth-2021-0123 | MathSciNet: MR4415978
  2. On the Saxl graphs of primitive groups with soluble stabilisers
    joint with T.C. Burness
    Algebraic Combinatorics 5 (2022), 1053-1087.
    arXiv: 2105.11861 | doi: 10.5802/alco.238 | MathSciNet: MR4511160
  3. On base sizes for primitive groups of product type
    joint with T.C. Burness
    Journal of Pure and Applied Algebra 227 (2023), Paper No. 107228, 43 pp.
    arXiv: 2202.02816 | doi: 10.1016/j.jpaa.2022.107228 | MathSciNet: MR4478370
  4. Base sizes of primitive groups of diagonal type
    Forum of Mathematics, Sigma 12 (2024), Paper No. e2, 43 pp.
    arXiv: 2303.14290 | doi: 10.1017/fms.2023.121 | MathSciNet: MR4685056
  5. Finite permutation groups of rank \(3\)
    joint with C.H. Li and Y.Z. Zhu
    22 pages, submitted
    arXiv: 2311.04057


  1. On valency problems of Saxl graphs of almost simple primitive groups with soluble stabiliser
    Supervisor: Professor Cai Heng Li
    Undergraduate thesis, SUSTech (2020) [pdf]