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 $.
Citation: Ximin Wang, Zheng Huang, Xiaogang Zhang, Weijun Liu. A note on the Cameron-Praeger conjecture[J]. Electronic Research Archive, 2026, 34(4): 2243-2260. doi: 10.3934/era.2026101
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 $.
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Ximin Wang, Zheng Huang, Xiaogang Zhang, Weijun Liu. A note on the Cameron-Praeger conjecture[J]. Electronic Research Archive, 2026, 34(4): 2243-2260. doi: 10.3934/era.2026101
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