The \(E(2,A)\) sections of \(SL(2,A)\)

DOI10.2307/2944335zbMath0743.20048OpenAlexW2313072697MaRDI QIDQ1177435

Douglas L. Costa, Gordon E. Keller

Publication date: 26 June 1992

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2944335

zbMATH Keywords

elementary matricesnormal subgroupsquasi-idealnormal subgroup structure\(E(2,A)\)-normalized subgroupsclassical linear groups over ringsradices

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Chains and lattices of subgroups, subnormal subgroups (20E15) Other matrix groups over rings (20H25) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (19)

Normal subgroups of 𝑆𝐿(2,𝐴) ⋮ On Jordan ideals and matrix rings ⋮ The \(E_ 2(R)\)-normalized subgroups of \(\text{GL}_ 2(R)\) ⋮ An $\mathrm {A}_2$-proof of structure theorems for Chevalley groups of types $\mathrm {E}_6$ and $\mathrm {E}_7$ ⋮ Linear groups over general rings. I: Generalities. ⋮ Overgroups of elementary symplectic groups ⋮ Symplectic commutator subgroups. ⋮ Standardness and standard automorphisms of Chevalley groups. I: The case of rank at least two. ⋮ Conjugation-invariant norms on SL ₂ ( R ) for rings of S-algebraic integers with infinitely many units ⋮ Commutators of congruence subgroups in the arithmetic case ⋮ Overgroups of $\mathrm{EO}(n,R)$ ⋮ Abstract Radices ⋮ On special congruence subgroups of symplectic groups. ⋮ The E-normal structure of odd dimensional unitary groups ⋮ $\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$ ⋮ Unipotent matrices, modulo elementary matrices, in \(\text{SL}_2\) over a coordinate ring ⋮ Steinberg groups for Jordan pairs: an introduction with open problems ⋮ On the normal structure of the general linear group over a ring ⋮ Basic reductions in the description of normal subgroups.

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