Finite groups have distributive lattices of thick subcategories in the bounded derived category of their finite-dimensional representations over an algebraically closed field of characteristic p precisely when they are p-nilpotent.
Cohomology of modules in the principal block of a finite group.New York J
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Ore's theorem for thick subcategories
Finite groups have distributive lattices of thick subcategories in the bounded derived category of their finite-dimensional representations over an algebraically closed field of characteristic p precisely when they are p-nilpotent.