非交换有限单群的共交图直径为二
Co-intersection graphs of nonabelian finite simple groups have diameter two
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中文总结 AI 辅助
本文证明非交换有限单群的共交图连通且直径为二，并探讨有限群由共交图决定的程度及可实现的图类。
中文摘要 AI 辅助
设 $G$ 为有限群。$G$ 的共交图 $\Delta_G ^c$ 以 $G$ 的非平凡真子群为顶点，当两个子群交集平凡时，它们之间连边。显然，$\Delta_G ^c$ 的每个连通分支的直径至多为三。在本文中，我们证明当 $T$ 为非交换有限单群时，$\Delta_T$ 连通且直径恰好为二。我们还就有限群由其共交图决定的程度以及作为共交图出现的有限图类做了若干观察。
英文摘要
Let $G$ be a finite group. The co-intersection graph $Δ_G ^c$ of $G$ has as its vertices the nontrivial proper subgroups of $G$, with edges joining those pairs of subgroups which intersect trivially. It is clear that every connected component of $Δ_G ^c$ has diameter at most three. In this Note, we show that when $T$ is a nonabelian finite simple group, $Δ_T$ is connected of diameter exactly two. We also make several observations about the extent to which a finite group is determined by its co-intersection graph, and about the class of finite graphs arising as co-intersection graphs.
发表机构
- Christ’s College, University of Cambridge（剑桥大学基督学院）
- University of Manchester（曼彻斯特大学）
- Heilbronn Institute for Mathematical Research（海尔布伦数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
