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Apr 27, 2021 at 13:32 comment added naf Thanks for the clarification. My question was actually motivated by reading Chap IV, since I wanted to know if the results there could be formulated and proved over a more general base.
Apr 27, 2021 at 13:28 comment added Piotr Achinger Sorry, I meant Prop. 1.8 in Chap. II. But indeed it only treats smooth groups. In chapter IV they seem to make claims about p-torsion which may imply what you want.
Apr 27, 2021 at 10:00 comment added naf Thanks. Which Proposition 1.8 did you mean? There are two (at least) and I don't see how either of them immediately gives an answer to my question.
Apr 27, 2021 at 6:40 history answered Piotr Achinger CC BY-SA 4.0