Subgroups of direct products of elementarily free groups

被引：11
|
作者：
Bridson, Martin R.
Howie, James
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England
[2] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2007年 / 17卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
limit groups; homological finiteness properties; Bass-Serre theory;
D O I：
10.1007/s00039-007-0600-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The structure of groups having the same elementary theory as free groups is now known: they and their finitely generated subgroups form a prescribed subclass E of the hyperbolic limit groups. We prove that if G(1),..., G(n) are in E then a subgroup Gamma subset of G(1) x... x G(n) is of type FPn if and only if Gamma is itself, up to finite index, the direct product of at most n groups from E. This provides a partial answer to a question of Sela.
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页码：385 / 403
页数：19
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