论文标题
有限简单组的交点图最多为5
The intersection graph of a finite simple group has diameter at most 5
论文作者
论文摘要
令$ g $为非亚伯有限的简单组。此外，令$δ_g$为$ g $的交点图，其顶点是$ g $的适当的非平凡亚组，当它们非正式地相交时，当它们与边缘相交时，其截然不同的子组与边缘连接在一起。我们证明$Δ_g$的直径为5的紧密上限为5，从而解决了Shen（2010）提出的问题。此外，只有婴儿怪物群和某些奇数质子的统一组才能达到5个直径。
Let $G$ be a non-abelian finite simple group. In addition, let $Δ_G$ be the intersection graph of $G$, whose vertices are the proper nontrivial subgroups of $G$, with distinct subgroups joined by an edge if and only if they intersect nontrivially. We prove that the diameter of $Δ_G$ has a tight upper bound of 5, thereby resolving a question posed by Shen (2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.
