Subgroups of Word Hyperbolic Groups in Dimension 2
Subgroups of Word Hyperbolic Groups in Dimension 2
复制标题
2 维词双曲群的子群
DOI：
10.1112/jlms/54.2.261
复制
发表时间：
1996
影响因子：
1.2
通讯作者：
S. Gersten
中科院分区：
文献类型：
--
作者：
S. Gersten
若G是上同调维数为2的字双曲群，则G的FP 2型子群也是字双曲群。定义了FP 2型群的等周不等式，并证明了在此广义情形下的线性等周不等式等价于词双曲性。给出了一般图的双曲性的一个充分条件，并将其沿着应用于“相对双曲性”。Lyndon双曲型小消去群的显式子群是字双曲群。双曲1-关系子群的显式子群是双曲的。自由伯恩赛德群的显示子群在稳定值域内是有限的.
If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 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.