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	On the automorphism groups of quasiprimitive almost simple graphs
	Fang, XG ; Havas, G ; Praeger, CE
	1999
关键词	2-ARC TRANSITIVE GRAPHS PERMUTATION-GROUPS FINITE
英文摘要	Let Gamma be a graph and let G be a subgroup of automorphisms of Gamma. Then G is said to be locally primitive on Gamma if, for each vertex upsilon, the stabilizer G(upsilon) induces a primitive group of permutations on the set of vertices adjacent to upsilon. This paper investigates pairs (Gamma, G) for which G is locally primitive on Gamma, G is an almost simple group (that is, L less than or equal to G less than or equal to Aut(L) for some nonabelian simple group L), and the simple socle L is transitive on vertices. Each such graph is a cover of a possibly smaller graph <(Gamma)over tilde> on which G is also locally primitive, and for which in addition Aut <(Gamma)over tilde> is quasiprimitive on vertices (that is, every nontrivial normal subgroup of Aut <(Gamma)over tilde> is vertex-transitive). it is proved that Aut <(Gamma)over tilde> is also an almost simple group. Tn the general case in which Aut Gamma is not quasiprimitive on vertices, we show that either every intransitive minimal normal subgroup of Aut Gamma centralizes L, or L is of Lie type and Aut Gamma involves an explicitly known same characteristic module for L. (C) 1999 Academic Press.; Mathematics; SCI(E); 6; ARTICLE; 1; 271-283; 222
语种	英语
出处	SCI
出版者	journal of algebra
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157367]
专题	数学科学学院
推荐引用方式 GB/T 7714	Fang, XG,Havas, G,Praeger, CE. On the automorphism groups of quasiprimitive almost simple graphs. 1999-01-01.

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