On the Automorphism Groups of Quasiprimitive Almost Simple Graphs
On the Automorphism Groups of Quasiprimitive Almost Simple Graphs
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DOI：
10.1006/jabr.1999.8020
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发表时间：
1999-12
影响因子：
0.9
通讯作者：
X. Fang;G. Havas;C. Praeger
中科院分区：
文献类型：
--
作者：
X. Fang;G. Havas;C. Praeger
设Gamma是一个图，G是Gamma的一个自同构子群.则称G在Gamma上是局部本原的，如果对于每个顶点uppermise，稳定子G（uppermise）在与uppermise相邻的顶点集合上诱导出一个置换的本原群。本文研究了（Gamma，G）对，其中G是Gamma上的局部本原，G是几乎单群（即对某个非交换单群L，L小于或等于G小于或等于Aut（L）），单脚柱L在点上可迁.每个这样的图是一个可能更小的图l（Gamma）在tildeg上的覆盖，在这个图上G也是局部本原的，并且对于这个图，Aut l（Gamma）在tildeg上在顶点上是拟本原的（即，Aut l（Gamma）在tildeg上的每个非平凡正规子群是点传递的）。证明了Tildeg上的Aut l（Gamma）也是几乎单群.在Aut Gamma在顶点上不是拟本原的一般情况下，我们证明了要么Aut Gamma的每个不传递极小正规子群集中于L，要么L是Lie型的且Aut Gamma包含L的一个显式已知的相同特征模. (C)北京：科学出版社.
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 l(Gamma)over tildeg on which G is also locally primitive, and for which in addition Aut l(Gamma)over tildeg is quasiprimitive on vertices (that is, every nontrivial normal subgroup of Aut l(Gamma)over tildeg is vertex-transitive). it is proved that Aut l(Gamma)over tildeg 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.