论文标题
$ pgl_2（p^{2^n}）$的订单综合体可签约
The order complex of $PGL_2(p^{2^n})$ is contractible when $p$ is odd
论文作者
论文摘要
给定一个$ g $，其子组的晶格$ \ mathcal {l}（g）$可以以自然方式看作是一种简单的复合体。包含$ 1_g，g \ in \ Mathcal {l}（g）$意味着$ \ nathcal {l}（g）$是可违约的，因此我们研究了该订单复杂$ \ wideHat {\ Mathcal {\ Mathcal {l}（l}（l}（l}（g）}（g）（g）}：= \ Mathcal = \ natcal {l l} g）的拓扑结构， \ {1_g，g \} $。在此简短的说明中，我们考虑$ \ wideHat {\ Mathcal {l}（g）} $的同质类型，其中$ g \ cong pgl_2（p^{2^n}）$，$ p \ geq 3 $，$ n \ geq 1 $，并显示$ \ \ widehat {\ wideHat {\ nathcal contrib contria这与有限基团的同阶阶络合物类型的Shareshian的猜想是一致的。
Given a group $G$, its lattice of subgroups $\mathcal{L}(G)$ can be viewed as a simplicial complex in a natural way. The inclusion of $1_G, G \in \mathcal{L}(G)$ implies that $\mathcal{L}(G)$ is contractible, and so we study the topology of the order complex $\widehat{\mathcal{L}(G)} := \mathcal{L}(G) \setminus \{1_G,G\}$. In this short note we consider the homotopy type of $\widehat{\mathcal{L}(G)}$ where $G \cong PGL_2(p^{2^n})$, $p \geq 3$, $n \geq 1$ and show that $\widehat{\mathcal{L}(G)}$ is contractible. This is consistent with a conjecture of Shareshian on the homotopy type of order complexes of finite groups.
