The p-adic group ring of SL2(pf)

In the present article we show that the Zp[ζpf−1]-order Zp[ζpf−1]SL2(pf) can be recognized among those orders whose reduction modulo p is isomorphic to FpfSL2(pf) using only ring-theoretic properties. In other words we show that FpfSL2(pf) lifts uniquely to a Zp[ζpf−1]-order, provided certain reasonable conditions are imposed on the lift. This proves a conjecture made by Nebe in [8] concerning the basic order of Z2[ζ2f−1]SL2(2f).