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PreprintCC BY 4.0arXiv

The classification of non-solvable transitive BLT-sets of 𝒬(4,q)

  • Weicong Li
  • Qing Xiang
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Abstract

For an odd prime power q, a BLT-set ℬ is a set of (q+1) points of 𝒬(4,q) such that every point of 𝒬(4,q) is collinear with at most two points of ℬ. We complete the classification of BLT-sets of 𝒬(4,q) admitting a non-solvable transitive automorphism group. Nelson and Penttila completed the classification of BLT-sets ℬ with a non-solvable transitive automorphism group acting irreducibly on the underlying $5$-dimensional vector space. In this paper, we prove that a BLT-set with a non-solvable transitive full automorphism group acting reducibly on the underlying $5$-dimensional vector space is either a classical BLT-set or a Kantor semifield BLT-set.

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Cite

BibTeXRIS
BibTeX
@misc{li2026classification,
  title = {{The classification of non-solvable transitive BLT-sets of $\mathcalQ(4,q)$}},
  author = {Weicong Li and Qing Xiang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04876},
  eprint = {2610.04876},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04876},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The classification of non-solvable transitive BLT-sets of 𝒬(4,q)
AU  - Weicong Li
AU  - Qing Xiang
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.04876
UR  - https://arxiv.org/abs/2610.04876
AB  - For an odd prime power q, a BLT-set ℬ is a set of (q+1) points of 𝒬(4,q) such that every point of 𝒬(4,q) is collinear with at most two points of ℬ. We complete the classification of BLT-sets of 𝒬(4,q) admitting a non-solvable transitive automorphism group. Nelson and Penttila completed the classification of BLT-sets ℬ with a non-solvable transitive automorphism group acting irreducibly on the underlying $5$-dimensional vector space. In this paper, we prove that a BLT-set with a non-solvable transitive full automorphism group acting reducibly on the underlying $5$-dimensional vector space is either a classical BLT-set or a Kantor semifield BLT-set.
ER  -