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Research Article | Open Access

A note on the Cameron-Praeger conjecture

Ximin Wang1, Zheng Huang1( ), Xiaogang Zhang1, Weijun Liu2
Department of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, China
College of Education, Guangdong University of Science and Technology, Guangdong 523083, China
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Abstract

The Cameron-Praeger conjecture stands as a central problem at the intersection of group theory and combinatorial design, and has inspired sustained research by mathematicians worldwide for decades. In this paper, we took a step forward in the proof of the Cameron-Praeger conjecture. We studied a special case of the famous Cameron-Praeger conjecture in design theory and proved that there are no block-transitive 6- ( v , k , 2 ) designs with k dividing v.

Keywords

Cameron-Praeger conjectureblock-transitiveCamina-Gagen condition6-designs3-homogeneous permutation groups

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Electronic Research Archive
Volume 34 Issue 4,
April 2026
Pages 2243-2260
DOI: 10.3934/era.2026101

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Cite this article:
Wang X, Huang Z, Zhang X, et al. A note on the Cameron-Praeger conjecture. Electronic Research Archive, 2026, 34(4): 2243-2260. https://doi.org/10.3934/era.2026101

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Received: 03 November 2025
Revised: 26 February 2026
Accepted: 28 February 2026
Published: 15 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)