# 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 propertiesVIEW 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 |