The Normal Subgroup Structure of the Picard Group

DOI10.2307/2000868zbMath0624.20031OpenAlexW4256372237MaRDI QIDQ3762502

Morris Newman, Benjamin Fine

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000868

zbMATH Keywords

principal congruence subgroupssubgroups of finite indexmodular groupPicard groupderived seriesnormal subgroup latticecongruence subgroup latticenormal noncongruence subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Structure of modular groups and generalizations; arithmetic groups (11F06) Chains and lattices of subgroups, subnormal subgroups (20E15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Derived series, central series, and generalizations for groups (20F14)

Related Items

Unnamed Item, On subgroups of \(GL_ 2\) over Banach algebras and von Neumann regular rings which are normalized by elementary matrices, Linear groups over general rings. I: Generalities., Normal subgroups of symplectic groups over rings, Free quotients of subgroups of the Bianchi groups whose kernels contain many elementary matrices, Totally geodesic hyperbolic 3-manifolds in hyperbolic link complements of tori in \(S^4\), A generalization of the parametrized modular group, On the structure of \(GL_ 2\) over stable range one rings, Power subgroups of some Hecke groups., Normal subgroups of 𝑃𝑆𝐿₂(𝑍[√-3)]

Cites Work

• Unnamed Item
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• Polyhedral groups and graph amalgamation products
• Free quotients and the congruence kernel of \(SL_ 2\).
• Free subgroups and normal subgroups of the modular group
• Fuchsian Embeddings in the Bianchi Groups
• Classifying Torsion-Free Subgroups of the Picard Group
• Congruence Subgroups of the Picard Group
• Fuchsian Subgroups of the Picard Group
• The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
• Subgroups of HNN Groups and Groups with one Defining Relation
• Normal Congruence Subgroups of the Modular Group
• A Complete Description of the Normal Subgroups of Genus One of the Modular Group