Thin buildings (in the sense of Tits) arise as coset geometries of Coxeter groups, most of the spherical buildings as coset geometries of groups with a BN-pair. We generalize the notion of a group to ``generalized groups" in such a way that arbitrary (not necessarily thin or spherical) buildings arise as coset geometries of ``generalized Coxeter groups". Each set of right cosets of a subgroup of a given group turns out to be a generalized group. These generalized groups are called ``schurian". We are looking for sufficient criteria for generalized groups to be schurian. Tits' Reduction Theorem for thick spherical buildings of rank at least $3$ translates into such a criterion. This observation suggest an alternate proof of Tits' theorem within generalized group theory.

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