support

Let $R[G]$ be the group ring of a group $G$ over a ring $R$.

Let $x={\sum }_g{x}_{g}g$ be an element of $R[G]$. The support of $x$, often written $\mathrm{supp}(x)$, is the set of elements of $G$ which occur with non-zero coefficient in the expansion of $x$.

Thus:

$$\mathrm{supp}(x)=\{g\in G\mid x_g\ne 0\}.$$