Arithmetic groups with isomorphic finite quotients |
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Authors: | Menny Aka |
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Affiliation: | Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel |
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Abstract: | 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 fibers are of unbounded size. |
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