Burnside group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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This term is related to: combinatorial group theory
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Definition

Definition with symbols

The Burnside group B(n,d) (sometimes called the free Burnside group) is defined as the quotient of the free group on n generators by the normal subgroup generated by all d^{th} powers. A Burnside group is a group that occurs as B(n,d) for some choice of d and n.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finitely generated free group Burnside group B(n,0) |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finitely generated group
Reduced free group |FULL LIST, MORE INFO