Word problem for groups

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History

Normal forms Max Dehn Conjugacy problem Group isomorphism problem Fundamental groups

16 related topics

Examples

Automatic groups Finite groups Negatively curved (aka. hyperbolic) groups Euclidean groups Coxeter groups

13 related topics

Algebraic structure and the word problem

Algebraic structure Boone–Higman theorem Bernhard Neumann Angus Macintyre Algebraically closed group

8 related topics

A more concrete description

Rewriting Literal strings Null string Identity element Cyclic group

6 related topics

Topics to explore

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Overview

Mathematics
Abstract algebra
Combinatorial group theory
Finitely generated group
Undecidable problems Undecidable problem
Finite set
Generators Generating set of a group
Formal language
Free monoid with involution
Presentation Presentation of a group
Recursively enumerable

History

Normal forms Normal form (abstract rewriting)
Max Dehn
Conjugacy problem
Group isomorphism problem
Fundamental groups Fundamental group
Dehn's algorithm Small cancellation theory
Decision problems Decision problem
Pyotr Novikov
William Boone William Boone (mathematician)
Mathematical logic
Theory of algorithms
Polycyclic groups Polycyclic group
Todd–Coxeter algorithm
Knuth–Bendix completion algorithm
Dehn's algorithm
Torus

A more concrete description

Examples

Automatic groups Automatic group
Finite groups Finite group
Negatively curved (aka. hyperbolic) groups Negatively curved group
Euclidean groups Euclidean group
Coxeter groups Coxeter group
Braid groups Braid group
Geometrically finite groups Geometrically finite group
Free groups Free group
Free abelian groups Free abelian group
Absolutely presented groups Absolute presentation of a group
Simple groups Simple group
Residually finite
One-relator groups One-relator group

Partial solution of the word problem

If and only if
Natural numbers Natural number
Locally finite Locally finite group
Pseudocode

Unsolvability of the uniform word problem

Algebraic structure and the word problem

Algebraic structure
Boone–Higman theorem Boone–Higman theorem?action=edit&redlink=1
Bernhard Neumann
Angus Macintyre
Algebraically closed group
Kuznetsov Alexander Kuznetsov (mathematician)
Quotient groups Quotient group
Trivial group

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Map overview Semantic statistics

Nodes68

Edges67

Triples2

Avg. degree1.97

Density0.029412

Components1

How this topic connects Entity context

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