Premium
Subgroups of Word Hyperbolic Groups in Dimension 2
Author(s) -
Gersten S. M.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/54.2.261
Subject(s) - mathematics , isoperimetric inequality , hyperbolic group , relatively hyperbolic group , word (group theory) , word problem (mathematics education) , finitely generated group , dimension (graph theory) , pure mathematics , stallings theorem about ends of groups , context (archaeology) , graph , finitely generated abelian group , type (biology) , group (periodic table) , hyperbolic manifold , combinatorics , hyperbolic function , mathematical analysis , arithmetic , geometry , paleontology , biology , ecology , chemistry , organic chemistry
If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP 2 is also word hyperbolic. Isoperimetric inequalities are defined for groups of type FP 2 and it is shown that the linear isoperimetric inequality in this generalized context is equivalent to word hyperbolicity. A sufficient condition for hyperbolicity of a general graph is given along with an application to ‘relative hyperbolicity’. Finitely presented subgroups of Lyndon's small cancellation groups of hyperbolic type are word hyperbolic. Finitely presented subgroups of hyperbolic 1‐relator groups are hyperbolic. Finitely presented subgroups of free Burnside groups are finite in the stable range.