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

Abstract

We introduce and study a subring SC of $\mathbb{Z}S{L}_2({\mathbb{F}}_q)$ obtained by summing elements of $S{L}_2({\mathbb{F}}_q)$ according to their support. The ring SC can be used for the construction of several association schemes.