Let G be a reductive group scheme over the p-adic integers, and let $$\mu $$ minuscule cocharacter for G. In Hodge-type case, we construct functor from nilpotent $$(G,\mu )$$ -displays p-nilpotent rings R to formal p-divisible groups equipped with crystalline Tate tensors. When R/pR has p-basis étale locally, show that this defines an equivalence between two categories. The definition of relies...

In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups. Section