We prove that the \(\mathbb {F}_p[[t]]\)-standard Hausdorff spectrum of a compact \(\mathbb {F}_p[[t]]\)-analytic group contains a real interval and that it coincides with the full unit interval when the group is soluble. Moreover, we show that the \(\mathbb {F}_p[[t]]\)-standard Hausdorff spectrum of classical Chevalley groups over \(\mathbb {F}_p[[t]]\) is not full, since 1 is an isolated point thereof.

中文翻译：

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紧致$$ \ mathbb {F} _p [[t]] $$ F p [[t]]分析组的标准Hausdorff谱

我们证明了紧致\（\ mathbb {F} _p [[t]] \）分析组的\（\ mathbb {F} _p [[t]] \）-标准Hausdorff谱包含一个实区间，并且当基团可溶时，它与整个单位间隔一致。此外，我们显示，\（\ mathbb {F} _p [[T]] \） -标准古典Chevalley群的豪斯多夫光谱的经\（\ mathbb {F} _p [[T]] \）不充分，由于图1是其孤立点。