论文标题
Pro-$ p $组，具有完全正常的Hausdorff Spectra
A pro-$p$ group with full normal Hausdorff spectra
论文作者
论文摘要
对于每个奇数$ p $，我们生产$ 2 $生成的pro- p $ p $ g $ g $，其正常的hausdorff spectra \ [\ mathrm {hspec} _ {\ trianglelefteq}^{\ trianglelefteq}^{\ mathcal \ Mathrm {hdim} _ {g}^{\ Mathcal {s}}（H）\ Mid H \ Trianglelefteq_ \ Mathrm {C} G \} \]相对于五个五个标准过滤系列$ \ MATHCAL {s} $ sermistion suberies $ s $ s $ - $ P $ - 功率系列，迭代$ P $ - 功率系列和Frattini系列 - 都等于完整的单位间隔$ [0,1] $。这里$ \ mathrm {hdim} _g^{\ mathcal {s}} \ colon \ {x \ s \ mid x \ subseteq g \} \ to [0,1] $表示与自然转换式计量$ fifltration $ n Mather $ \ \ \ \ \ \ maths $ nsation $相关的hausdorff dimension $ \ \ \ \ s $。
For each odd prime $p$, we produce a $2$-generated pro-$p$ group $G$ whose normal Hausdorff spectra \[ \mathrm{hspec}_{\trianglelefteq}^{\mathcal{S}}(G) = \{ \mathrm{hdim}_{G}^{\mathcal{S}}(H)\mid H\trianglelefteq_\mathrm{c} G \} \] with respect to five standard filtration series $\mathcal{S}$ - namely the lower $p$-series, the dimension subgroup series, the $p$-power series, the iterated $p$-power series and the Frattini series - are all equal to the full unit interval $[0,1]$. Here $\mathrm{hdim}_G^{\mathcal{S}} \colon \{ X\mid X \subseteq G \} \to[0,1]$ denotes the Hausdorff dimension function associated to the natural translation-invariant metric induced by the filtration series $\mathcal{S}$.
