Primitive permutation groups with a solvable 2-transitive subconstituent

JOURNAL OF ALGEBRA

卷:386

Article

Wang, Jie^1,2 

[1] Peking Univ, LMAM, Beijing 100871, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

关键词: Primitive groups;    2-transitive subconstituent;    Almost simple groups;    Affine groups;    Solvable maximal subgroups;   

DOI  :  10.1016/j.jalgebra.2013.03.028

来源: Elsevier

【 摘 要 】

For a permutation group G acting on a finite set Omega and a point alpha is an element of Omega, a suborbit Delta(alpha) is an orbit of the point stabilizer G(alpha) on Omega. The permutation group induced by G(alpha) on Delta(alpha) is called a subconstituent of G. Moreover, G is said to be uniprimitive if G is primitive but not 2-transitive. In this paper we investigate uniprimitive permutation groups which have a solvable 2-transitive subconstituent. We determine all such groups G which have a simple socle. The affine case, that is G has an elementary abelian socle, are also discussed and an infinite family of affine primitive groups with non-self-paired 2-transitive subconstituents are presented. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free