Cohomological properties of the profinite completion of Bianchi groups
نویسندگان
چکیده
We prove that the Bianchi groups, that is the groups PSL(2,O) where O is the ring of integers in an imaginary quadratic number field, are good. This is a property introduced by J.P. Serre which relates the cohomology groups of a group to those of its profinite completion. We also develop properties of goodness to be able to show that certain natural central extensions of Fuchsian groups are residually finite. A result which contrasts examples of Deligne who shows that the analogous central extensions of Sp(4, Z) do not have this property. 2000 Mathematics Subject Classification: Primary 20F28, 20E05; Secondary 20E36, 20F34, 20G05
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