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Questions on group theory which concern finite groups.

4 votes

Looking for criterion for $\mathbb{Z}G$-modules to be projective

You need to assume projectivity for all primes $p$, otherwise stupid counterexamples are easily found with $G$ the trivial group. Assuming this, then for any finitely generated $\mathbb Z G$-module $ …
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5 votes

Is the Gelfand-Graev character isomorphic to a cohomology group for some sheaf on a Deligne-...

This is not precisely what you're looking for, but Bonnafé and Rouquier have made in "Coxeter orbits and modular representations." Nagoya Math. J., 183 :1–34, 2006, the conjecture that the DL-restric …
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  • 686