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Hyperbolic generalized triangle groups, property (T) and finite simple quotients

Caprace, Pierre-Emmanuel; Conder, Marston; Kaluba, Marek 1; Witzel, Stefan
1 Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)

Abstract:

We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those hyperbolic Kazhdan groups possess finite simple quotient groups of arbitrarily large rank; they constitute the first-known specimens combining those properties. All the hyperbolic groups we consider are non-positively curved k-fold generalized triangle groups, that is, groups that possess a simplicial action on a CAT(0) triangle complex, which is sharply transitive on the set of triangles, and such that edge-stabilizers are cyclic of order k.


Verlagsausgabe §
DOI: 10.5445/IR/1000149968
Veröffentlicht am 16.08.2022
Originalveröffentlichung
DOI: 10.1112/jlms.12668
Scopus
Zitationen: 1
Web of Science
Zitationen: 1
Dimensions
Zitationen: 1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 12.2022
Sprache Englisch
Identifikator ISSN: 0024-6107, 1469-7750
KITopen-ID: 1000149968
Erschienen in Journal of the London Mathematical Society
Verlag John Wiley and Sons
Band 106
Heft 4
Seiten 3577-3637
Vorab online veröffentlicht am 05.08.2022
Nachgewiesen in Dimensions
Web of Science
Scopus
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