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Let K be a field and g(K) a Chevalley group (scheme) over K. Let (B,N) be thestandard spherical BN-pair in g(K), with T=B\cap N and Weyl group W=N/T. Weprove that there exist non-trivial elements w\in W such that allrepresentatives of w in N have finite order. This allows us to exhibit examplesof subgroups of g(Q_p) that act Weyl transitively but not strongly transitivelyon the affine building Delta associated with g(Q_p). Such examples werepreviously known only in the case when g(Q_p)=SL_2(Q_p) and Delta is a tree.

Strongly and Weyl transitive group actions on buildings arising from Chevalley groups