解析pro-$p$群的下$p$-级数与Hausdorff维数
群论
2025-09-11 v3
摘要
设为维-adic解析pro-群。我们构造了一个近似级数，该级数在层中规则下降，且其项与下-级数的偏差一致有界。这揭示了一组新的有理不变量，它们自然关联于，给出了上述一致界，并限制了的闭子群关于下-级数的Hausdorff维数的可能取值。特别地，关于下-级数的Hausdorff谱是离散的，且至多包含个有理数。
关键词
引用
@article{arxiv.2402.06876,
title = {The lower $p$-series of analytic pro-$p$ groups and Hausdorff dimension},
author = {Iker de las Heras and Benjamin Klopsch and Anitha Thillaisundaram},
journal= {arXiv preprint arXiv:2402.06876},
year = {2025}
}
备注
23 pages; this is the Author Accepted Manuscript version of the following article: I. de las Heras, B. Klopsch and A. Thillaisundaram, The lower p-series of analytic pro-p groups and Hausdorff dimension, J. Lond. Math. Soc. 112 (2) (2025), which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.70271