Determining Fuchsian groups by their finite quotients

Show simple item record Bridson, MR en Conder, Marston en Reid, AW en 2016-10-18T04:09:54Z en 2016-07 en
dc.identifier.citation Israel Journal of Mathematics, 2016, 214(1), pp. 1-41 en
dc.identifier.issn 0021-2172 en
dc.identifier.uri en
dc.description.abstract Let C(Γ) be the set of isomorphism classes of the finite groups that are quotients (homomorphic images) of Γ. We investigate the extent to which C(Γ) determines Γ when Γ is a group of geometric interest. If Γ1 is a lattice in PSL(2, R) and Γ2 is a lattice in any connected Lie group, then C(Γ1) = C(Γ2) implies that Γ1 ≅ Γ2. If F is a free group and Γ is a right-angled Artin group or a residually free group (with one extra condition), then C(F) = C(Γ) implies that F ≅ Γ. If Γ1 < PSL(2, C) and Γ2 < G are nonuniform arithmetic lattices, where G is a semisimple Lie group with trivial centre and no compact factors, then C(Γ1) = C(Γ2) implies that G ≅ PSL(2, C) and that Γ2 belongs to one of finitely many commensurability classes. These results are proved using the theory of profinite groups; we do not exhibit explicit finite quotients that distinguish among the groups in question. But in the special case of two non-isomorphic triangle groups, we give an explicit description of finite quotients that distinguish between them. en
dc.description.uri en
dc.publisher Springer Verlag (Germany) en
dc.relation.ispartofseries Israel Journal of Mathematics en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from en
dc.rights.uri en
dc.subject Science & Technology en
dc.subject Physical Sciences en
dc.subject Mathematics en
dc.subject BIANCHI GROUPS en
dc.subject PRODUCTS en
dc.subject PROPERTY en
dc.subject GEOMETRY en
dc.title Determining Fuchsian groups by their finite quotients en
dc.type Journal Article en
dc.identifier.doi 10.1007/s11856-016-1341-6 en
pubs.issue 1 en
pubs.begin-page 1 en
pubs.volume 214 en
dc.description.version AM - Accepted Manuscript en
dc.rights.holder Copyright: Hebrew University of Jerusalem en en
pubs.end-page 41 en
pubs.publication-status Published en
dc.rights.accessrights en
pubs.subtype Article en
pubs.elements-id 540980 en Science en Mathematics en
dc.identifier.eissn 1565-8511 en
pubs.record-created-at-source-date 2016-10-18 en

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