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Aug 27, 2018 at 19:20 comment added Andy Putman @DerekHolt: I would assume so. There are two possibilities, depending on whether you want the associated graded to be a restricted Lie algebra over $\mathbb{F}_p$ or only an ordinary Lie algebra over $\mathbb{F}_p$. In most situations, you want it to be a restricted one (and that is what is covered in the reference I gave).
Aug 27, 2018 at 18:03 comment added Derek Holt And is it the same as the lower $p$-central series? I had never heard of the mod $p$ lower central series.
Aug 27, 2018 at 15:39 history answered Andy Putman CC BY-SA 4.0