Blocks with transitive fusion systems
  Suppose that all nontrivial subsections of a $p$-block $B$ are conjugate (where $p$ is a prime). By using the classification of the finite simple groups, we prove that the defect groups of $B$ are either extraspecial of order $p^3$ with $p \in \{3,5\}$ or elementary abelian. 
L\'azl\'o H\'ethelyi, Radha Kessar, Burkhard K\"ulshammer, and   Benjamin Sambale
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