摘要
After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is usually easy by the theorem of Delandtsheer and Doyen.The primitive ones are now subdivided,according to the O'Nan-Scotte theorem and some further work by Camina,into the socles which are an elementary abelian or non-abelian simple.In this paper,we consider the latter.Namely,T ≤ G ≤ Aut(T) and G acts line-transitively on finite linear spaces,where T is a non-abelian simple.We obtain some useful lemmas.In particular,we prove that when T is isomorphic to 3D4(q),then T is line-transitive,where q is a power of the prime p.
After the classification of flag-transitive linear spaces, attention has now turned to line-transitive linear spaces. Such spaces are first divided into the point-imprimitive and the point-primitive, the first class is usually easy by the theorem of Delandtsheer and Doyen. The primitive ones are now subdivided, according to the O'Nan-Scotte theorem and some further work by Camina, into the socles which are an elementary abelian or non-abelian simple. In this paper, we consider the latter. Namely, T≤G≤Aut(T) and G acts line-transitively on finite linear spaces, where T is a non-abelian simple. We obtain some useful lemmas. In particular, we prove that when T is isomorphic to 3D4(q), then T is line-transitive, where q is a power of the prime p.
基金
This work was supported by the National Natural Science Foundation of China (Grant No.10471152).
