Finiteness Properties of S-Arithmetic Groups - a Survey

Details Finiteness Properties of S-Arithmetic Groups - a Survey Finiteness Properties of S-Arithmetic Groups - a Survey

2002-12-29

arxiv.org/abs/math/0212366v1

Mathematics

Group Theory

28 pages, 5 figures

Scientific paper

We give an overview about finiteness properties of soluble S-arithmetic
groups. Both, the number field case and the function field case are covered.
The main result is: If B is a Borel subgroup in a Chevalley group and R is an
S-arithmetic ring, then the group B(R) has finiteness length |S|-1 in the
function field case, and infinite finiteness length in the number field case.

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