摘要
线传递线性空间可以分为非点本原和点本原两种情形,而点本原的情况又可以分成基柱为初等交换群或非交换单群两种情形.本文考虑后一种情形,即T是非交换单群,T≤G≤Aut(T)且G线传递,点本原作用在有限线性空间上的情形.证明了当T同构于F_4(q)时,若T_L不是~2F_4(q),B_4(q),D_4(q).S_3,~3D_4(q).3,F_4(q^(1/2))和T的抛物子群的子群时,T也是线传递的,这里q是素数p的方幂.
Line-transitively linear spaces are first divided into the point-imprimitive and the point-primitive, and the primitive ones are now subdivided into the socles which are elementary abelian or non-abelian simple. In this paper, the latter is considered. Namely, T is non-abelian simple, T ≤ G ≤ Aut（T） and G acts line-transitively on finite linear spaces. And we prove that when T is isomorphic to F4（q）, if TL is not the subgroups of 2F4 （q）, B4 （q）, D4 （q）· S3,^3D4 （q）. 3, F4 （q 1/2 ） or of the parabolic subgroups of T, T is also line-transitive, where q is a power of the prime p.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2010年第2期341-348,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10871205)
湖南省教育厅科研课题(09C444)
关键词
线传递
线性空间
自同构
几乎单群
line-transitive
linear space
automorphism
almost simple
