Burnside group

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