30,912 research outputs found
Subgroups of direct products of two limit groups
If S is a subgroup of a direct product of two limit groups, and S is of type
FP(2) over the rationals, then S has a subgroup of finite index that is a
direct product of at most two limit groups.Comment: 18 pages, no figure
Residually free 3-manifolds
We classify those compact 3-manifolds with incompressible toral boundary
whose fundamental groups are residually free. For example, if such a manifold
is prime and orientable and the fundamental group of is non-trivial
then , where is a surface.Comment: 19 pages, referee's comments incorporated, to appear in Algebraic &
Geometric Topolog
Subgroups of direct products of elementarily free groups
We exploit Zlil Sela's description of the structure of groups having the same
elementary theory as free groups: they and their finitely generated subgroups
form a prescribed subclass E of the hyperbolic limit groups.
We prove that if are in E then a subgroup is of type \FP_n if and only if is itself,
up to finite index, the direct product of at most groups from .
This answers a question of Sela.Comment: 19 pages, no figure
Normalisers in Limit Groups
Let \G be a limit group, S\subset\G a subgroup, and the normaliser of
. If has finite \Q-dimension, then is finitely
generated and either is finite or is abelian. This result has
applications to the study of subdirect products of limit groups.Comment: 10 pages, no figure
Subgroups of direct products of limit groups
If are limit groups and is of
type \FP_n(\mathbb Q) then contains a subgroup of finite index that is
itself a direct product of at most limit groups. This settles a question of
Sela.Comment: 20 pages, no figures. Final version. Accepted by the Annals of
Mathematic
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