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Jun 20 at 7:34 comment added Geoff Robinson @YCor: Indeed that is the case( and is done in Gorenstein).
Jun 20 at 7:00 comment added YCor I guess it's true for any action of a finite group of order coprime to $p$?
Jun 19 at 20:22 comment added Geoff Robinson Glad you found the precise reference.
Jun 19 at 20:01 comment added Nathan Dunfield Thanks! The precise reference in Gorenstein is Theorem 5.2.2 on page 176.
Jun 19 at 20:00 vote accept Nathan Dunfield
Jun 19 at 19:34 history answered Geoff Robinson CC BY-SA 4.0