Year: 2026
Type: preprint
Abstract: For an odd prime power $q$, a BLT-set $\mathcal B$ is a set of $(q+1)$ points of $\mathcal Q(4,q)$ such that every point of $\mathcal Q(4,q)$ is collinear with at most two points of $\mathcal B$. We complete the classification of BLT-sets of $\mathcal Q(4,q)$ admitting a non-solvable transitive automorphism group. Nelson and Penttila completed the classification of BLT-sets $\mathcal B$ 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.
Source: arXiv (Cornell University)
Authors: Li, Weicong, Xiang, Qing
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7840208982
OpenAlex ID: W7220698937