The order complex of $PG{L}_2(p^{2^n})$ is contractible when $p$ is odd

Emilio Pierro

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 $\mat…