dc.contributor.author |
Bridson, MR |
en |
dc.contributor.author |
Conder, Marston |
en |
dc.contributor.author |
Reid, AW |
en |
dc.date.accessioned |
2016-10-18T04:09:54Z |
en |
dc.date.issued |
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 |
http://hdl.handle.net/2292/30794 |
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 |
http://link.springer.com/journal/11856 |
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 http://www.sherpa.ac.uk/romeo/issn/0021-2172/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.subject |
Science & Technology |
en |
dc.subject |
Physical Sciences |
en |
dc.subject |
Mathematics |
en |
dc.subject |
PROFINITE COMPLETIONS |
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dc.subject |
SUBGROUP SEPARABILITY |
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dc.subject |
SURFACE SUBGROUPS |
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dc.subject |
ELEMENTARY THEORY |
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 |
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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 |
pubs.author-url |
http://link.springer.com/article/10.1007/s11856-016-1341-6 |
en |
pubs.end-page |
41 |
en |
pubs.publication-status |
Published |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
540980 |
en |
pubs.org-id |
Science |
en |
pubs.org-id |
Mathematics |
en |
dc.identifier.eissn |
1565-8511 |
en |
pubs.record-created-at-source-date |
2016-10-18 |
en |