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.
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Literatur
RANKIN, R.A.: Subgroups of the modular group defined by a single linear congruence. Acta Arith.24, 313–323 (1973/74).
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Wolfart, J., Spilker, J. Untergruppen der GL2, welche durch homogene lineare Kongruenzen definiert sind. Manuscripta Math 14, 349–378 (1975). https://doi.org/10.1007/BF01169266
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DOI: https://doi.org/10.1007/BF01169266