Group satisfying a quadratic isoperimetric inequality

From Groupprops
Jump to: navigation, search

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