A *diagonalizable group scheme* $G$ is a group scheme satisfying the following equivalent conditions: 1. $G$ is the [[Cartier duality|Cartier dual]] of a [[constant group scheme]]. 1. $O(G)$ is a [[character|character group]] i.e. $O(G)$ is generated morphisms $G\to \mu_k$ into the [[multiplicative group scheme]].