Pushout of quasi-finite and flat group schemes over a Dedekind ring

AbstractLet G, G1 and G2 be quasi-finite and flat group schemes over a complete discrete valuation ring R, φ1:G→G1 any morphism of R-group schemes and φ2:G→G2 a model map. We construct the pushout P of G1 and G2 over G in the category of R-affine group schemes. In particular when φ1 is a model map too we show that P is still a model of the generic fibre of G. We also provide a short proof for the existence of cokernels and quotients of finite and flat group schemes over any Dedekind ring