A non-abelian free pro-\(p\) group is not linear over a local field

DOI10.1006/jabr.1998.7682zbMath0923.20018OpenAlexW2020472010MaRDI QIDQ1283280

K. Appert

Publication date: 25 August 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7682

zbMATH Keywords

free pro-\(p\) groupslinear pro-\(p\) groups over local fields

Mathematics Subject Classification ID

Linear algebraic groups over local fields and their integers (20G25) Limits, profinite groups (20E18)

Related Items (7)

Dimension and randomness in groups acting on rooted trees ⋮ GOLOD–SHAFAREVICH GROUPS: A SURVEY ⋮ Galois groups of tamely ramified \(p\)-extensions ⋮ On some pro-\(p\) groups from infinite-dimensional Lie theory ⋮ The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field ⋮ On pro-2 identities of 2×2 linear groups ⋮ On linear just infinite pro-\(p\) groups

Cites Work

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• Powerful \(p\)-groups. I: Finite groups.
• Group presentation, p-adic analytic groups and lattices in \(SL_ 2({\mathbb{C}})\)
• Non-Abelian free pro-\(p\)-groups cannot be represented by 2-by-2 matrices
• Lie algebras and Lie groups. 1964 lectures, given at Harvard University.
• Compact subgroups of linear algebraic groups
• On some \(\Lambda\)-analytic pro-\(p\) groups
• Finite presentations of pro-\(p\) groups and discrete groups
• Profinite Groups, Arithmetic, and Geometry. (AM-67)

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