We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson [41] showing that simple endotrivial modules of most groups come from quasi-simple groups.
The inductive blockwise Alperin weight condition is a system of conditions whose verification for all non-abelian finite simple groups would imply the blockwise Alperin weight conjecture. We establish this condition for the groups G 2 (q), q 5, and 3 D 4 (q) for all primes dividing their order.
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