Seeking for a converse to a well-known theorem by Borel-Tits, we address the question whether the group of rational points G(k) of an anisotropic reductive k-group may admit a split spherical BN-pair. We show that if k is a perfect field or a local field, then such a BN-pair must be virtually trivial. We also consider arbitrary compact groups and show that the only abstract BN-pairs they can admit are spherical, and even virtually trivial provided they are split.

翻译：为了与Borel-Tits的著名论调反调,我们探讨了一个问题,即一个厌异还原K组的G(k)理性点组是否可以接受分裂球形的BN-pair。我们表明,如果 k 是完美的场或局部场,那么这样的BN-pair就几乎是微不足道的。我们还考虑到任意的紧凑组,并表明他们能够承认的唯一抽象的BN-pair是球形的,只要是分裂的,甚至几乎是微不足道的。