The lower p $p$ -series of analytic pro- p $p$ groups and Hausdorff dimension

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-24 DOI:10.1112/jlms.70271

Iker de las Heras, Benjamin Klopsch, Anitha Thillaisundaram

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引用次数: 0

Abstract

Let $G$ be a $p$ -adic analytic pro- $p$ group of dimension $d$ , with lower $p$ -series $L : P_{i} (G), i \in N$ . We produce an approximate series which descends regularly in strata and whose terms deviate from $P_{i} (G)$ in a uniformly bounded way. This brings to light a new set of rational invariants $ξ_{1}, …, ξ_{d} \in [1 / d, 1]$ , canonically associated to $G$ , such that

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解析前p$ p$群的下p$ p$ -级数与Hausdorff维数

设G$ G$是维数为d$ d$的p$ p$一元解析亲p$ p$群，其下p$ p$ -级数为L：P i(G), i∈N $\mathcal {L} \冒号P_i(G), \,i \in \mathbb {N}$。我们得到了一个近似级数，它在地层中有规律地下降，其项以一致有界的方式偏离pi (G)$ P_i(G)$。这就引出了一组新的有理不变量ξ 1，…，ξ d∈[1 / d,1]$ \xi _1, \ldots, \xi _d \in [\nicefrac {1}{d},1]$，通常与G$ G$相关联，使得

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.