On the verbal width of finitely generated pro-\(p\) groups.

DOI10.4171/RMI/549zbMath1158.20012arXivmath/0302018MaRDI QIDQ951992

Andrei Jaikin-Zapirain

Publication date: 5 November 2008

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0302018

zbMATH Keywords

finitely generated profinite groupspro-\(p\) groups\(p\)-adic analytic groupsverbal subgroupsverbal widths

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Analysis on (p)-adic Lie groups (22E35) Limits, profinite groups (20E18)

Related Items (17)

Book Review: Words: notes on verbal width in groups ⋮ Strong conciseness of coprime commutators in profinite groups ⋮ On verbal subgroups of adelic groups. ⋮ Ellipticity of words ⋮ Bounding the order of a verbal subgroup in a residually finite group ⋮ Conciseness in compact \(R\)-analytic groups ⋮ Random generation of finite and profinite groups and group enumeration. ⋮ Powers in finite groups. ⋮ Pro‐p groups of positive rank gradient and Hausdorff dimension ⋮ Variations on a theme of Burns and Medvedev. ⋮ Verbal width in the Nottingham group and related Lie algebras ⋮ Surjectivity of word maps on special linear groups of degree 2 ⋮ Engel groups in bath - ten years later ⋮ Words of Engel type are concise in residually finite groups. II. ⋮ Strong conciseness in profinite groups ⋮ Geometry of word equations in simple algebraic groups over special fields ⋮ Words of Engel type are concise in residually finite groups

Cites Work

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• On finitely generated profinite groups. I: Strong completeness and uniform bounds. II: Products in quasisimple groups.
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• The entropy of graded algebras
• Variations on a theme of Burns and Medvedev.
• Some approximative integration formulas of degree 3 for an \(n\)-dimensional simplex
• Closed Subgroups of Profinite Groups
• Two-Generator conditions for Residually Finite Groups
• Hausdorff dimension, pro-𝑝 groups, and Kac-Moody algebras
• Analytic relatively free pro-p groups
• Varieties of groups
• Subgroups of finite index in profinite groups

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