A reduction theorem establishes that the blockwise Galois Alperin weight conjecture follows from inductive conditions on simple groups via isomorphisms of H-triples.
Linckelmann,The Block Theory of Finite Group Algebras, volume II
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A reduction theorem for the blockwise Navarro Alperin weight conjecture via H-triples
A reduction theorem establishes that the blockwise Galois Alperin weight conjecture follows from inductive conditions on simple groups via isomorphisms of H-triples.