Steiner 5-设计上的Camina-Gagen定理

Camina-Gagen theorem for Steiner 5-designs

著名的Camina-Gagen定理表明,若群G是一个满足k整除v的2-(v,k,1)设计的区传递的自同构群,则G是旗传递的.本文将这个定理推广到5-(v,k,1)设计上,并证明了如果群G区传递地作用在一个非平凡的5-(v,k,1)设计上且满足k整除v,则G是旗传递的.

A famous Camina-Gagen theorem is that if G acts as a block-transitive group of automorphisms of a 2-(v,k,1)design with k|v,then G is flag-transitive.In this paper,we generalize this theorem to 5-(v,k,1)designs.We prove that if G acts block-transitively on a non-trivial 5-(v,k,1)design D with k|v,then D is flag-transitive.