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We introduce and study a subring $\mathcal{SC}$ of $\mathbbZ[\mathrm{SL}\_2(\mathbb F\_q)]$ obtained by summing elements of$\mathrm{SL}\_2(\mathbb F\_q)$ according to their support. The ring $\mathcalSC$ can be used for the construction of several association schemes.

The Ring of Support-Classes of $\mathrm{SL}\_2(\mathbb F\_q)$