In this note, there is the following theorem:
[Theorem 4.4] Let $\mathscr{G}$ be a separated $R$-group scheme of finite type such that its open relative identity component $\mathscr{G}^0$ is semi-abelian, and assume that its generic fiber $A$ is an abelian variety. The natural map $f:\mathscr{G}\rightarrow N=N(A)$ is an open immersion.
where $R$ is a discrete valuation ring.
Under the hypotheses, the author concluded that both $\mathscr{G}$ and $N$ are integral $R$-schemes at the end of page 12. I don't understand why $\mathscr{G}$ is.