Group satisfying a quadratic isoperimetric inequality
From Groupprops
Contents
Definition
A group satisfying a quadratic isoperimetric inequality is a finitely presented group (or recursively presented group, may be?) having an isoperimetric function whose growth rate is (at most) quadratic.
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
Relation with other properties
Stronger properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
biautomatic group | Automatic group|FULL LIST, MORE INFO | |||
automatic group | |FULL LIST, MORE INFO | |||
combable group | |FULL LIST, MORE INFO | |||
finitely generated free group | |FULL LIST, MORE INFO | |||
finitely generated abelian group | |FULL LIST, MORE INFO |
Weaker properties
Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
group satisfying a polynomial isoperimetric inequality | ||||
group with nondeterministic polynomial-time solvable word problem | ||||
group with solvable word problem | Group satisfying a polynomial isoperimetric inequality, Group with nondeterministic polynomial-time solvable word problem|FULL LIST, MORE INFO |