3 problems

Let $G$ be a finite group and let $p$ be a prime. Let $\mathcal{S}_p(G)$ be the poset of all non-trivial $p$-subgroups of $G$, and let $\operatorname{O}_p(G)$ be the largest normal…

Let $G$ be a finite group such that $G=AF^*(G)$, where $A$ is an elementary abelian $p$-subgroup of rank $r\geq 3$, and let $F^*(G)$ be the direct product of the $A$-conjugates of…

Stronger Webb conjecture. The finite space