3 problems

Serwene's conjecture. Let $\mathcal{F}$ be a saturated fusion system. For any finite group $G$ having an $\mathcal{F}$-block $b$, it follows that $\mathcal{F}$ is realizable.

Let $G$ be a finite group, let $k$ be an algebraically closed field of prime characteristic $p>0$ dividing $|G|$, and let $kGb$ be a block algebra with defect group $P$. Choose a d…

Let $p$ be a prime, let $k$ be an algebraically closed field of characteristic $p$, let $G$ be a finite group, and let $B$ be a block algebra of $kG$. A block has defect at most…