Remark

Let G be a group which is not necessarily commutative with a filtration $(G_n)_{n \in \mathbf{Z}}$ such that $G_{n+1}$ is normal in G, for all $n \in \mathbf{Z}$; again let $\mathrm{gr}_n(G) = G_n/G_{n+1}$. The restricted product of the family $(\mathrm{gr}_n(G))_{n \in \mathbf{Z}}$, that is the subgroup of the product $\prod_{n \in \mathbf{Z}} \mathrm{gr}_n(G)$ consisting of the elements $(\xi_n)$ all of whose components, except at most a finite number, are equal to the identity element, is also called the graded group associated with G and denoted by $\mathrm{gr}(G)$.