Primitive permutation groups of bounded orbital diameter
Primitive permutation groups of bounded orbital diameter
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DOI：
10.1112/plms/pdp024
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发表时间：
2010-01-01
影响因子：
1.8
通讯作者：
Tent, Katrin
中科院分区：
文献类型：
--
作者：
Liebeck, Martin W.;Macpherson, Dugald;Tent, Katrin
本文给出了有限本原置换群的无限族的一个刻画，使得所有轨道图的直径存在一个一致的有限上界。这等价于描述有限置换群的族，使得族的每个超积都是本原的。一个关键的结果是，在几乎简单的情况下，柱脚的固定李秩，除了非常特殊的情况下，有这样一个直径界。这是证明使用最近的结果的模型理论的伪有限域和差域。
We give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs. This is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive. A key result is that, in the almost simple case with socle of fixed Lie rank, apart from very specific cases, there is such a diameter bound. This is proved using recent results on the model theory of pseudofinite fields and difference fields.