Amalgams of type \(F_ 3\) (Q1108377)

In [Groups and Graphs (1985; Zbl 0566.20013)] the author and \textit{B. Stellmacher} investigated groups possessing a weak BN-pair. They showed that with a few exceptions the parabolic subgroups are uniquely determined up to isomorphism. One of these exceptions was the system of type \(F_ 3\). In the paper under review the author proves that the parabolic system of type \(F_ 3\) is unique up to isomorphism. For doing this he uses the geometric description of the \(F_ 3\)-amalgam to establish generators and relations for the amalgam and so for the parabolics. This system of generators and relations turns out to be unique.