Association schemes in which the thin residue is a finite cyclic group
Association schemes in which the thin residue is a finite cyclic group
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薄残差是有限循环群的关联方案
DOI：
10.1016/j.jalgebra.2010.04.013
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
P. Zieschang
中科院分区：
文献类型：
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作者：
P. Zieschang
在本文中，我们研究了有限集上的关联方案S，其中每个元素S满足ss _ _ S ={S}。如果s的闭子集s s与s∈s的交的偏序集是分配的，则这些方案是舒里图式。（如果一个方案（以一种很容易理解的方式）产生于一个传递置换群，那么它就被称为舒里图式。）如果这些方案是舒里型的，则它们所由的传递置换群具有次正规的一点稳定子。由第一个结果可知，如果方案的薄残数是薄的，并且有一个分配的正规闭子集格（正规子群格），则方案是舒里的。这意味着，例如，如果方案的薄残基是一个环群，那么方案就是舒里图式。
In this article, we investigate association schemes S (on finite sets) in which each element s satisfies ss⁎s={s}. It is shown that these schemes are schurian if the partially ordered set of the intersections of the closed subsets s⁎s of S with s∈S is distributive. (A scheme is said to be schurian if it arises (in a well-understood way) from a transitive permutation group.) It is also shown that, if these schemes are schurian, the transitive permutation group from which they arise have subnormal one-point stabilizers. As a consequence of the first result one obtains that schemes are schurian if their thin residue is thin and has a distributive normal closed subset lattice (normal subgroup lattice). This implies, for instance, that schemes are schurian if their thin residue is a cyclic group.