In this short note we study the cohomology algebra of saturated fusion systems using finite groups which realize saturated fusion systems and Hochschild cohomology of group algebras. A similar result to a theorem of Alperin is proved for varieties of cohomology algebras of fusions systems associated to block algebras of finite groups.
Normal restriction in finite groups
Cohomology of algebraic groups, finite groups, and Lie algebras: Interactions and Connections
Beauville surfaces and finite groups
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