Finitely generated group

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Applications

Švarc-Milnor lemma Action Geometric group theory Topological Geometric

29 related topics

Subgroups

Commutator subgroup Schreier index formula Albert G. Howson Intersection Hanna Neumann

14 related topics

Finitely generated abelian groups

Abelian group Module Ring Finitely generated abelian group Linear combination

10 related topics

Examples

Canonical projection Cyclic Isomorphic Integers Locally cyclic group

9 related topics

Topics to explore

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Overview

Algebra
Group Group (mathematics)
Finite Finite set
Generating set Generating set of a group
Inverses Inverse element
Finite group
Countable Countable set
Rational numbers Rational number

Examples

Canonical projection Quotient group
Cyclic Cyclic group
Isomorphic Group isomorphism
Integers Integer
Locally cyclic group
Subgroup
Free group
A fortiori Argumentum a fortiori
§Examples Presentation of a group

Finitely generated abelian groups

Abelian group
Module Module (mathematics)
Ring Ring (mathematics)
Finitely generated abelian group
Linear combination
Fundamental theorem of finitely generated abelian groups
Direct sum Direct sum of groups
Free abelian group
Rank Rank of an abelian group
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Subgroups

Applications

Švarc-Milnor lemma Švarc–Milnor lemma
Action Group action
Geometric group theory
Topological Topology
Geometric Geometry
Spaces Space (mathematics)
Fundamental groups Fundamental group
Manifolds Manifold
CAT(0) CAT(0) group
Myers' theorem Myers's theorem
Mostow's rigidity theorem Mostow rigidity theorem
Hyperbolic manifolds Hyperbolic manifold
Riemannian isometry Isometry (Riemannian geometry)
Mapping class groups of surfaces Mapping class group of a surface
In p-adic groups Lattice (discrete subgroup)
Superrigidity
Margulis' arithmeticity theorem Arithmetic group
Expander graphs Expander graph
Property T Kazhdan's property (T)
Combinatorial group theory
Group-based cryptography
Random walks on graphs Random walk
Cayley graphs Cayley graph
Percolation Percolation theory
Crystallographic groups Crystallographic group
Molecular symmetry groups Molecular symmetry
Topological quantum field theories
Knot groups Knot group
Molecular knots Molecular knot

Related notions

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Map overview Semantic statistics

Nodes83

Edges82

Triples23

Avg. degree1.98

Density0.024096

Components1

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Finitely generated group

Top relations

related to Differential geometry and topology · 7

Finitely generated group → CAT, Fundamental, Mapping, Mostow's, Myers, Riemannian, Their

has application · 3

Finitely generated group → Finitely, Geometric, Milnor

related to Examples · 3

Finitely generated group → Every, Examples, The

is a · 2

Finitely generated group → decision problem of whether two words in the generators of the group represent the same element, group G that has some finite generating set S so that every element of G can be written as the combination

related to Combinatorics, algorithmics and cryptography · 2

Finitely generated group → Infinite, TAlgorithmic

related to Probability theory · 2

Finitely generated group → Cayley, Random

related to Related notions · 2

Finitely generated group → By, The

related to Subgroups · 2

Finitely generated group → On, The

Important terminology Word statistics

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Important terminology

group generated finitely every groups finite subgroup subgroups abelian generators element locally examples theory countable free fundamental theorem two set

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Finitely generated group	is a	group G that has some finite generating set S so that every element of G can be written as the combination	0.90	text
Finitely generated group	is a	decision problem of whether two words in the generators of the group represent the same element	0.90	text
Finitely generated group	has application	Finitely	0.60	section
Finitely generated group	has application	Milnor	0.60	section
Finitely generated group	has application	Geometric	0.60	section
Finitely generated group	related to Combinatorics, algorithmics and cryptography	Infinite	0.60	section
Finitely generated group	related to Combinatorics, algorithmics and cryptography	TAlgorithmic	0.60	section
Finitely generated group	related to Differential geometry and topology	Fundamental	0.60	section
Finitely generated group	related to Differential geometry and topology	Their	0.60	section
Finitely generated group	related to Differential geometry and topology	CAT	0.60	section
Finitely generated group	related to Differential geometry and topology	Myers	0.60	section
Finitely generated group	related to Differential geometry and topology	Mostow's	0.60	section

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Applications

Subgroups

Finitely generated abelian groups

Examples

Key facts & relationships

Topics to explore

Overview

Examples

Finitely generated abelian groups

Subgroups

Applications

Related notions

Advanced semantic analysis

Map overview Semantic statistics

Finitely generated group

How this topic connects Entity context

Finitely generated group

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges