Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Arithmetic group

In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example S L 2 ( Z ) . {\displaystyle \mathrm {SL} _{2}(\mathbb {Z} ).} They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of…

History & Applications

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Arithmetic group. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

History

Definition and construction

Examples

Arithmetic lattices in semisimple Lie groups

S-arithmetic groups

Some applications

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Arithmetic group

Nodes74
Edges73
Triples51
Avg. degree1.97
Density0.027027
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Arithmetic group

Top relations

related to Examples · 13
Arithmetic group → Bianchi, Blumenthal, For, GL, Hilbert, Other, PGL, PSL, Siegel, Similar, SL, Sp, The
related to history · 11
Arithmetic group → Arithmetic, Charles Hermite, Hermann Minkowski, Hermitian, Langlands, Minkowski's, Of, One, Siegel, The, This
related to Explicit expander graphs · 8
Arithmetic group → Arithmetic, Kazhdan's, Lubotzky, Lubotzky-Phillips-Sarnak, Margulis, Ramanujan, Such, Zimmer
related to Isospectral manifolds · 4
Arithmetic group → Arithmetic, Marie-France Vignéras, The, This
related to The congruence subgroup problem · 4
Arithmetic group → It, Jean-Pierre Serre, The, These
related to Using number fields · 4
Arithmetic group → GL, If, Indeed, On
related to Lattices in Lie groups over local fields · 3
Arithmetic group → Gamma, Harish-Chandra, The Borel
related to Definition · 2
Arithmetic group → GL, The
is a · 1
Arithmetic group → group obtained as the integer points of an algebraic group

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle arithmetic mathrm groups mathbb group lattice lattices example number sl theory subgroup lie algebraic theorem margulis gl defined obtained

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Arithmetic groupis agroup obtained as the integer points of an algebraic group0.90text
the discriminantinstance ofThe topic was related to Minkowski's geometry of numbers and the early development of the study of arithmetic invariants of number fields0.80text
Arithmetic grouprelated to DefinitionThe0.60section
Arithmetic grouprelated to DefinitionGL0.60section
Arithmetic grouprelated to ExamplesThe0.60section
Arithmetic grouprelated to ExamplesSL0.60section
Arithmetic grouprelated to ExamplesPSL0.60section
Arithmetic grouprelated to ExamplesGL0.60section
Arithmetic grouprelated to ExamplesPGL0.60section
Arithmetic grouprelated to ExamplesFor0.60section
Arithmetic grouprelated to ExamplesSimilar0.60section
Arithmetic grouprelated to ExamplesSiegel0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.