Alternating groups and point-primitive linear spaces with number of points being squarefree

作者：Guan, Haiyan^*; Zhou, Shenglin

来源：Journal of Combinatorial Designs, 2023, 31(5): 277-286.

DOI：10.1002/jcd.21879

• automorphism group
• finite regular linear space
• point-primitive

This paper is a further contribution to the classification of point-primitive finite regular linear spaces. Let S ${\mathscr{S}}$ be a nontrivial finite regular linear space whose number of points v $v$ is squarefree. We prove that if G <= Aut(S) $G\le \text{Aut}({\mathscr{S}})$ is point-primitive with an alternating socle, then S ${\mathscr{S}}$ is the projective space PG(3,2) $\text{PG}(3,2)$.