Subgroups of direct products of elementarily free groups

Martin R. Bridson; James Howie

doi:10.1007/s00039-007-0600-4

Subgroups of direct products of elementarily free groups

Martin R. Bridson
, James Howie

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

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 G ? G ₁ × ? × G _n is of type FP _n if and only if G 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. © Birkhäuser Verlag, Basel 2007.

Original language	English
Pages (from-to)	385-403
Number of pages	19
Journal	Geometric and Functional Analysis
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s00039-007-0600-4
Publication status	Published - Jun 2007

Keywords

Bass-Serre theory
Homological finiteness properties
Limit groups

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10.1007/s00039-007-0600-4

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AB - 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 G ? G 1 × ? × G n is of type FP n if and only if G 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. © Birkhäuser Verlag, Basel 2007.

KW - Bass-Serre theory

KW - Homological finiteness properties

KW - Limit groups

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DO - 10.1007/s00039-007-0600-4

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EP - 403

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

Subgroups of direct products of elementarily free groups

Abstract

Keywords

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