Arithmetic groups with isomorphic finite quotients
Group Theory
2011-10-25 v2
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 the fibers are of unbounded size.
Cite
@article{arxiv.1107.4147,
title = {Arithmetic groups with isomorphic finite quotients},
author = {Menny Aka},
journal= {arXiv preprint arXiv:1107.4147},
year = {2011}
}
Comments
Minor revisions. To appear in Journal of Algebra