Free quotients of congruence subgroups of SL2 over a Dedekind ring of arithmetic type contained in a function field

DOI10.1017/S0305004100066809zbMath0619.20030OpenAlexW1975382131MaRDI QIDQ3755651

Alexander W. Mason

Publication date: 1987

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100066809

zbMATH Keywords

subgroups of finite indexprincipal congruence subgroupDedekind ring of arithmetic typeq-elementary matricescoordinate rings of affine curvesfree quotient groupsfunction field in one variable over a finite field

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Structure of modular groups and generalizations; arithmetic groups (11F06) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Classical groups (11E57) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (12)

Free quotients of congruence subgroups of \(SL_ 2\) over a coordinate ring ⋮ Quotients of the congruence kernels of \(\text{SL}_ 2\) over arithmetic Dedekind domains ⋮ Linear groups over general rings. I: Generalities. ⋮ Normal subgroups of symplectic groups over rings ⋮ Non-normal, standard subgroups of the Bianchi groups ⋮ Groups generated by elements with rational fixed points ⋮ OnGL₂of a local ring in which 2 is not a unit II ⋮ Congruence hulls in \(SL_ n\) ⋮ Normal subgroups of \(SL_ 2(k[t)\) with or without free quotients] ⋮ Subnormal subgroups of E_n(R) have no free, non-abelian quotients, when n≧3 ⋮ Free quotients of congruence subgroups of the Serre groups and unipotent matrices ⋮ Free quotients of congruence subgroups of Bianchi groups

Cites Work

• Unnamed Item
• Free non-Abelian quotients of \(SL_ 2\) over orders of imaginary quadratic numberfields
• Free quotients and the congruence kernel of \(SL_ 2\).
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Zur \(\mathrm{SL}_2\) der ganzen Zahlen eines imaginär-quadratischen Zahlkörpers
• ANOMALOUS NORMAL SUBGROUPS OF SL₂(K[x)]

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