The congruence subgroup property for \(\Aut F_2\): a group-theoretic proof of Asada's theorem.

DOI10.4171/GGD/130zbMath1251.20035arXiv0909.0304OpenAlexW2084867702MaRDI QIDQ664236

Andrei S. Rapinchuk, Mikhail V. Ershov, Kai-Uwe Bux

Publication date: 29 February 2012

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.0304

zbMATH Keywords

subgroups of finite indexautomorphism groupsfree groupsprofinite completionscongruence subgroup property

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Automorphisms of infinite groups (20E36) Automorphism groups of groups (20F28) Free nonabelian groups (20E05) Limits, profinite groups (20E18)

Related Items (12)

Tamely ramified covers of the projective line with alternating and symmetric monodromy ⋮ The congruence subgroup problem for finitely generated nilpotent groups ⋮ A pro-\(l\) version of the congruence subgroup problem for mapping class groups of genus one ⋮ The congruence subgroup problem for the free metabelian group on two generators ⋮ Families of ϕ‐congruence subgroups of the modular group ⋮ Arithmetic Veech sublattices of SL\((2,\mathbf {Z})\) ⋮ Nonabelian level structures, Nielsen equivalence, and Markoff triples ⋮ The congruence subgroup problem for low rank free and free metabelian groups ⋮ On the Abelianizations of congruence subgroups of \(\Aut(F_2)\). ⋮ On the congruence subgroup problem for branch groups ⋮ The IA-congruence kernel of high rank free metabelian groups ⋮ The congruence subgroup problem for the free metabelian group on \(n\geq 4\) generators

Cites Work

• On finitely generated profinite groups. I: Strong completeness and uniform bounds. II: Products in quasisimple groups.
• Exactness properties of profinite completion functors
• Infinite generation of automorphism groups of free pro-\(p\) groups
• Characteristic subgroups and automorphisms of free profinite groups
• On the index of congruence subgroups of \(\Aut(F_n)\).
• On products of profinite groups
• Cohomological topics in group theory.
• Torsion elements and centralizers in free products of profinite groups.
• Configuration Spaces.
• The faithfulness of the monodromy representations associated with certain families of algebraic curves
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