The group ring of \(\text{SL}_2(p^2)\) over the \(p\)-adic integers (Q1279927)

The finite groups \(\text{SL}_2(p^s)\) and their representations have been intensely studied from a variety of viewpoints. In this paper, the author considers the case \(s=2\). She looks at the group ring \(R=\mathbb{Z}_p[\text{SL}_2(p^2)]\) and gives an explicit description of the basic order which is Morita equivalent to \(R\). Since the Cartan invariants of \(\text{SL}_2(p^2)\) are relatively small she is able to use the method of \textit{W. Plesken} [Group rings of finite groups over \(p\)-adic integers, Lect. Notes Math. 1026 (1983; Zbl 0537.20002)] to compute the graduated hull of \(R\) and in this way she is able to determine its irreducible lattices.