@article{Wang2026, 
author = {Ximin Wang and Zheng Huang and Xiaogang Zhang and Weijun Liu},
title = {A note on the Cameron-Praeger conjecture},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {4},
pages = {2243-2260},
keywords = {Cameron-Praeger conjecture, block-transitive, Camina-Gagen condition, 6-designs, 3-homogeneous permutation groups},
url = {https://www.sciopen.com/article/10.3934/era.2026101},
doi = {10.3934/era.2026101},
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.}
}