PreprintScale and tidy subgroups for Weyltransitive automorphism groups of buildingsU. Baumgartner and J. Parkinson and J. RamaggeAbstractWe consider closed, Weyltransitive groups of automorphisms of thick buildings. For each element of such a group, we derive a combinatorial formula for its scale and establish the existence of a tidy subgroup for it that equals the stabilizer of a simplex. Simplices whose stabilizers are tidy for some element of the group are characterizedin terms of the minimal set of the isometry induced by the element on the Davisrealisation of the building and in terms of the Weyldistance between them and their image. We use our results to derive some topological properties of closed, Weyltransitive groups of automorphisms. Keywords: Building, scale, tidy subgroup.AMS Subject Classification: Primary 22D05; secondary 52E24, 20E36, 20F65.
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