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Conditions for a $p$-divisible group to be represented by a formal Lie group

Let $S$ be a scheme where $p$ is locally nilpotent and let $G$ be a $p$-divisible group over $S$. Is connectedness of $G$ equivalent to $G[p] := \ker(p : G \to G) \to S$ radicial (universally injectiv …
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Definition of formal group functors

In the book by Demazure "Lectures on $p$-Divisible Groups" a formal group functor over a field $k$ is defined in II.4 as a functor $\operatorname{Mf}_k \to \operatorname{Grp}$ where $\operatorname{Mf} …
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