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On n-partite digraphical representations of finite groups
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2022-02-23 , DOI: 10.1016/j.jcta.2022.105606 Jia-Li Du 1 , Yan-Quan Feng 2 , Pablo Spiga 3
中文翻译:
关于有限群的 n 部对数表示
更新日期:2022-02-23
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2022-02-23 , DOI: 10.1016/j.jcta.2022.105606 Jia-Li Du 1 , Yan-Quan Feng 2 , Pablo Spiga 3
Affiliation
A group G admits an n-partite digraphical representation if there exists a regular n-partite digraph Γ such that the automorphism group of Γ satisfies the following properties:
- (1)
is isomorphic to G,
- (2)
acts semiregularly on the vertices of Γ and
- (3)
the orbits of on the vertex set of Γ form a partition into n parts giving a structure of n-partite digraph to Γ.
In this paper, for every positive integer n, we classify the finite groups admitting an n-partite digraphical representation.
中文翻译:
关于有限群的 n 部对数表示
如果存在正则n部有向图 Γ 使得自同构群,则群G承认n 部有向图表示Γ 满足以下性质:
- (1)
与G同构,
- (2)
半规则地作用于 Γ 和
- (3)
的轨道在 Γ 的顶点集上形成一个划分为n 个部分,给Γ 一个n部分有向图的结构。
在本文中,对于每个正整数n,我们对允许n部图表示的有限群进行分类。