Arithmetic groups with isomorphic finite quotients

Details Arithmetic groups with isomorphic finite quotients Arithmetic groups with isomorphic finite quotients

2011-07-21

arxiv.org/abs/1107.4147v2

Mathematics

Group Theory

Minor revisions. To appear in Journal of Algebra

Scientific paper

Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-arithmetic group to (the isomorphism class of) its profinite completion. We show that for a wide class of S-arithmetic groups, this map is finite to one, while the the fibers are of unbounded size.

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