A locally primitive 2-design is a 2-design admitting an automorphism group G with primitive local actions. It is proved that G is point-primitive, and either G is an almost simple group, or G acting on the points is an affine group.
Cite
@article{arxiv.2403.16822,
title = {Locally primitive block designs},
author = {Jianfu Chen and Peice Hua and Cai Heng Li and Yanni Wu},
journal= {arXiv preprint arXiv:2403.16822},
year = {2024}
}