Characterization of \(p\)-adic analytic groups in terms of wreath products

DOI10.1016/0021-8693(92)90185-OzbMath0745.20029MaRDI QIDQ1183291

Aner Shalev

Publication date: 28 June 1992

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

finite \(p\)-groupsrestricted Burnside problem\(p\)-adic analyticfinitely generated pro-\(p\)-grouppowerful open subgrouppowerful pro-\(p\)-groups

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Finite nilpotent groups, (p)-groups (20D15) Analysis on (p)-adic Lie groups (22E35) Limits, profinite groups (20E18)

Related Items (12)

On locally finite 𝑝-groups satisfying an Engel condition ⋮ Certain locally nilpotent varieties of groups ⋮ Power closure and the Engel condition ⋮ Galois-theoretic features for 1-smooth pro-p groups ⋮ Powerful \(3\)-Engel groups ⋮ Profinite groups with NIP theory andp-adic analytic groups ⋮ Dimension subgroups and \(p\)-th powers in \(p\)-groups. ⋮ The ranks of central factor and commutator groups ⋮ Pro-finite \(p\)-adic Lie algebras ⋮ On the verbal width of finitely generated pro-\(p\) groups. ⋮ Model theory of finite and pseudofinite groups ⋮ Milnor identities

Cites Work

• Powerful \(p\)-groups. I: Finite groups.
• Powerful \(p\)-groups. II: \(p\)-adic analytic groups
• On groups of polynomial subgroup growth
• The power structure of \(p\)-groups. I
• \(p\)-adic analytic groups
• Uniform Finiteness Conditions in Residually Finite Groups
• On Finitely Generated Soluble Groups With No Large Wreath Product Sections
• Residually finite groups of finite rank
• Polynomial Identities in Graded Group Rings, Restricted Lie Algebras and p-Adic Analytic Groups
• Finitely generated groups, 𝑝-adic analytic groups, and Poincaré series
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