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

2016/11/03 by Blok, Rieuwert J., Hoffman, Corneliu G
#20G35 #51E24 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1611.00982

Abstract

In this note we establish the existence of all Curtis-Tits groups and Phan groups with 3-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.

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