Groups acting simply transitively on vertex sets of hyperbolic triangular buildings

Lisa Carbone, Riikka Kangaslampi, Alina Vdovina

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We construct and classify all groups given by triangular presentations associated to the smallest thick generalized quadrangle that act simply transitively on the vertices of hyperbolic triangular buildings of the smallest non-trivial thickness. Our classification yields 23 non-isomorphic torsion-free groups (which were obtained in an earlier work) and 168 non-isomorphic torsion groups acting on one of two possible buildings with the smallest thick generalized quadrangle as the link of each vertex. In analogy with the $\widetilde {A}-2$ case, we find both torsion and torsion-free groups acting on the same building.

Original languageEnglish (US)
Pages (from-to)101-112
Number of pages12
JournalLMS Journal of Computation and Mathematics
Volume15
DOIs
StatePublished - Dec 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computational Theory and Mathematics

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