2 problems

Let $\mathcal{C}(PSL_2(\mathbb{F}_7))$ denote the coset poset of $PSL_2(\mathbb{F}_7)$, and let $H_3$ denote its third homology group. Third-homology conjecture. … The preceding di…

Let $[H,G]$ be an interval of finite groups, and let $C(H,G)$ denote the associated coset poset with order complex $\Delta(C(H,G))$. An interval $[H,G]$ is Boolean when its subgrou…