\begin{definition}[Definition:Gradation on Abelian Group]
Let $G$ be an abelian group.
Let $\Delta$ be a set.
A '''gradation of type $\Delta$''' on $G$ is a family of subgroups $\family {G_\lambda}_{\lambda \mathop \in \Delta}$ of which $G$ is the internal direct sum.
\end{definition}