PreprintCC BY 4.0arXiv
Three-point orbits of 2-transitive groups and their combinatorial applications
Abstract
Let G be a finite $2$-transitive permutation group. We determine the orbits of G on the unordered triples of its point set, together with the three-point stabilizer and its image inside S3, for every affine and almost simple family in the finite $2$-transitive classification. These data classify the G-invariant triple systems and the simple $2−(v,3,λ)$} designs admitting G, and yield in a uniform way the standard objects attached to them: the incidence and block graphs (with arc-transitivity and strong regularity in the Steiner case), the constant-weight and design codes, and the Schurian coherent configurations on triples.
Related
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BibTeX
@misc{zhang2026threepoint,
title = {{Three-point orbits of 2-transitive groups and their combinatorial applications}},
author = {Zhilin Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15340},
eprint = {2610.15340},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15340},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Three-point orbits of 2-transitive groups and their combinatorial applications
AU - Zhilin Zhang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15340
UR - https://arxiv.org/abs/2610.15340
AB - Let G be a finite $2$-transitive permutation group. We determine the orbits of G on the unordered triples of its point set, together with the three-point stabilizer and its image inside S_3, for every affine and almost simple family in the finite $2$-transitive classification. These data classify the G-invariant triple systems and the simple $2−(v,3,λ)$} designs admitting G, and yield in a uniform way the standard objects attached to them: the incidence and block graphs (with arc-transitivity and strong regularity in the Steiner case), the constant-weight and design codes, and the Schurian coherent configurations on triples.
ER -