Analytic pro-p groups of small dimensions

DOI10.1515/JGT.2009.006zbMath1183.20030arXiv0806.2968OpenAlexW2963165177MaRDI QIDQ3184188

Benjamin Klopsch, Jon González-Sánchez

Publication date: 13 October 2009

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.2968

zbMATH Keywords

open pro-\(p\) subgroupspotent filtrations\(p\)-adic analytic pro-\(p\) groups\(p\)-saturable subgroups\(p\)-adic Lie theory

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Derived series, central series, and generalizations for groups (20F14) Limits, profinite groups (20E18) Associated Lie structures for groups (20F40)

Related Items

Zeta functions of three-dimensional \(p\)-adic Lie algebras, Arithmetic groups, base change, and representation growth., On the self-similarity index of \(p\)-adic analytic pro-\(p\) groups, On hereditarily self-similar \(p\)-adic analytic pro-\(p\) groups, Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions, Index-stable compact \(p\)-adic analytic groups, Representation zeta functions of compact \(p\)-adic analytic groups and arithmetic groups, \({K}_{1}\)-congruences for three-dimensional Lie groups, Cryptographic multilinear maps using pro-\(p\) groups, Uniform groups and Lie algebras, Growth of Selmer groups and fine Selmer groups in uniform pro-\(p\) extensions, Intense Automorphisms of Finite Groups, Prime decomposition and the Iwasawa MU-invariant, Pro-\(p\) groups with constant generating number on open subgroups., Kirillov's Orbit Method forp-Groups and Pro-pGroups, Zeta functions associated to admissible representations of compact 𝑝-adic Lie groups, On pro-\(p\) groups with quadratic cohomology, On self-similarity of \(p\)-adic analytic pro-\(p\) groups of small dimension, Transition formulae for ranks of abelian varieties

Cites Work

• Omega subgroups of pro-\(p\) groups.
• Pro-\(p\) groups with linear subgroup growth.
• On the Lie theory of \(p\)-adic analytic groups
• On the structure of normal subgroups of potent \(p\)-groups.
• Analytic pro-\(p\) groups and their Lie algebras
• On \(p\)-saturable groups.
• Groups with less than \(n\) subgroups of index \(n\).
• The groups with order \(p^7\) for odd prime \(p\).
• Similarity Problem Over SL(n, Z p )