Untergruppen der GL2, welche durch homogene lineare Kongruenzen definiert sind

Abstract

We generalize a result of Rankin [1]: Let R be a p — adic valuation ring or one of its factor rings and let G be GL2(R) or SL2(R). Then for M∈ M2(R), GM:={s∈G| trace MS=O} is a group iff trace M=0 and det M satisfies a simple condition (det M=O in most cases). We give similar conditions for several homogeneous linear equations defining subgroups of G.