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Generating set of a group

In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.

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Overview

Finitely generated group

Examples

Free group

Semigroups and monoids

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Generating set of a group

Nodes50
Edges49
Triples5
Avg. degree1.96
Density0.04
Components1

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Generating set of a group

Top relations

related to Semigroups and monoids · 4
Generating set of a group → If, Indeed, Similarly, The
is a · 1
Generating set of a group → subset of the group set such that every element of the group can be expressed as a combination

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Important terminology

group displaystyle set generated generating langle rangle element finite finitely generators subgroup elements integers subset inverses mathbb every expressed groups

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Generating set of a groupis asubset of the group set such that every element of the group can be expressed as a combination0.90text
Generating set of a grouprelated to Semigroups and monoidsIf0.60section
Generating set of a grouprelated to Semigroups and monoidsThe0.60section
Generating set of a grouprelated to Semigroups and monoidsIndeed0.60section
Generating set of a grouprelated to Semigroups and monoidsSimilarly0.60section

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