Burnside group
From Groupprops
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This term is related to: combinatorial group theory
View other terms related to combinatorial group theory | View facts related to combinatorial group theory
Contents
Definition
Definition with symbols
The Burnside group (sometimes called the free Burnside group) is defined as the quotient of the free group on
generators by the normal subgroup generated by all
powers. A Burnside group is a group that occurs as
for some choice of
and
.
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 ![]() |
|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 |