Factorisation of Finite Groups and Graphs

图的组合结构受其 对称性，而对称性是由它的群精确描述的， 自同构上的自同构群作用之间的相互作用 顶点，边和其他配置，揭示了重要的图形 结构，特别是图因子分解的存在性。反过来，每当一个群有两个 独立的传递行为，这些行为特别是在 确定图自同构群和图因子分解。我们将对群分解族进行分类，特别是对单群，并应用于建立对称图的理论 因子分解，并研究Cayley图和置换群的2-闭包。

The combinatorial structure of a graph is strongly influenced by its symmetry, and the symmetry is described precisely by its group of automorphisms. Interplay between actions of the automorphism group on vertices, edges, and other configurations, reveals important graph structure, especially the existence of graph factorisations. In turn, a group factorisation arises whenever a group has two independent transitive actions, and these arise in particular while determining graph automorphism groups, and graph factorisations. We will classify families of group factorisations, especially for simple groups, and apply this to establish a theory of symmetrical graph factorisations, and to study Cayley graphs and 2-closures of permutation groups.