English

Realizations and properties of $3$-spherical Curtis-Tits Groups and Phan groups

Group Theory 2016-11-04 v1

Abstract

In this note we establish the existence of all Curtis-Tits groups and Phan groups with 33-spherical diagram as classified previously and investigate some of their geometric and group theoretic properties. Whereas it is known that orientable Curtis-Tits groups with spherical or non-spherical and non-affine diagram are almost simple, we show that non-orientable Curtis-Tits groups are acylindrically hyperbolic and therefore have infinitely many infinite-index normal subgroups. However, we also provide concrete examples of non-orientable Curtis-Tits groups whose quotients are finite simple groups of Lie type.

Keywords

Cite

@article{arxiv.1611.00982,
  title  = {Realizations and properties of $3$-spherical Curtis-Tits Groups and Phan groups},
  author = {Rieuwert J. Blok and Corneliu G Hoffman},
  journal= {arXiv preprint arXiv:1611.00982},
  year   = {2016}
}