Free quotients and the congruence kernel of \(SL_ 2\).

DOI10.1016/0021-8693(82)90263-0zbMath0495.20021OpenAlexW1983369941MaRDI QIDQ1169561

Alexander Lubotzky

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90263-0

zbMATH Keywords

subgroups of finite indexcongruence subgroupsTits buildingscongruence subgroup problemcongruence kernel of SL2free pro-finite groupfree subgroup of finite index

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Linear algebraic groups over global fields and their integers (20G30)

Related Items (22)

Genuine non-congruence subgroups of Drinfeld modular groups ⋮ The congruence subgroup problem for finitely generated nilpotent groups ⋮ On the congruence kernel for simple algebraic groups ⋮ Quotients of the congruence kernels of \(\text{SL}_ 2\) over arithmetic Dedekind domains ⋮ Adelic profinite groups ⋮ Linear groups over general rings. I: Generalities. ⋮ The euclidean bianchi group ⋮ Free quotients and the first Betti number of some hyperbolic manifolds ⋮ Free quotients of congruence subgroups of SL₂ over a Dedekind ring of arithmetic type contained in a function field ⋮ Normal subgroups of profinite groups of non-negative deficiency. ⋮ Free quotients of subgroups of the Bianchi groups whose kernels contain many elementary matrices ⋮ The congruence subgroup problem for low rank free and free metabelian groups ⋮ Combinatorial group theory for pro-p groups ⋮ The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field ⋮ On the concept of level for subgroups of \(\text{SL}_2\) over arithmetic rings ⋮ Lattices in rank one Lie groups over local fields ⋮ Linear groups ⋮ Subnormal subgroups of E_n(R) have no free, non-abelian quotients, when n≧3 ⋮ The IA-congruence kernel of high rank free metabelian groups ⋮ The congruence subgroup problem for the free metabelian group on \(n\geq 4\) generators ⋮ The Normal Subgroup Structure of the Picard Group ⋮ Presentations for QuaternionicS-Unit Groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Free non-Abelian quotients of \(SL_ 2\) over orders of imaginary quadratic numberfields
• Subgroups of free profinite groups and large subfields of Q
• On the congruence subgroup problem
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Free subgroups in linear groups
• Le problème des groupes de congruence pour \(SL_2\)
• Zur \(\mathrm{SL}_2\) der ganzen Zahlen eines imaginär-quadratischen Zahlkörpers
• Maximal Abelian Subgroups of the Symmetric Groups

This page was built for publication: Free quotients and the congruence kernel of \(SL_ 2\).