On subgroups of right angled Artin groups with few generators
On subgroups of right angled Artin groups with few generators
For each natural number d we construct a 3-generated group H_d, which is a subdirect product of free groups, such that the cohomological dimension of H_d is d. Given a group F and a normal subgroup N?F we prove that any right angled Artin group containing the special HNN-extension of F with respect to N must also contain F/N. We apply this to construct, for every d?N, a 4-generated group G_d, embeddable into a right angled Artin group, such that the cohomological dimension of G_d is 2 but the cohomological dimension of any right angled Artin group, containing G_d, is at least d. These examples are used to show the non-existence of certain "universal" right angled Artin groups.
We also investigate finitely presented subgroups of direct products of limit groups. In particular we show that for every n?N there exists ?(n)?N such that any n-generated finitely presented subgroup of a direct product of finitely many free groups embeds into the ?(n)-th direct power of the free group of rank 2. As another corollary we derive that any n-generated finitely presented residually free group embeds into the direct product of at most ?(n) limit groups.
subgroups of right angled artin groups, partially commutative groups, special hnn-extensions, cohomological dimension, residually free groups
675-688
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
29 April 2015
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Minasyan, Ashot
(2015)
On subgroups of right angled Artin groups with few generators.
International Journal of Algebra and Computation, 25 (4), .
(doi:10.1142/S0218196715500150).
Abstract
For each natural number d we construct a 3-generated group H_d, which is a subdirect product of free groups, such that the cohomological dimension of H_d is d. Given a group F and a normal subgroup N?F we prove that any right angled Artin group containing the special HNN-extension of F with respect to N must also contain F/N. We apply this to construct, for every d?N, a 4-generated group G_d, embeddable into a right angled Artin group, such that the cohomological dimension of G_d is 2 but the cohomological dimension of any right angled Artin group, containing G_d, is at least d. These examples are used to show the non-existence of certain "universal" right angled Artin groups.
We also investigate finitely presented subgroups of direct products of limit groups. In particular we show that for every n?N there exists ?(n)?N such that any n-generated finitely presented subgroup of a direct product of finitely many free groups embeds into the ?(n)-th direct power of the free group of rank 2. As another corollary we derive that any n-generated finitely presented residually free group embeds into the direct product of at most ?(n) limit groups.
Text
low_rank-7.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 30 March 2015
Published date: 29 April 2015
Keywords:
subgroups of right angled artin groups, partially commutative groups, special hnn-extensions, cohomological dimension, residually free groups
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 378725
URI: http://eprints.soton.ac.uk/id/eprint/378725
ISSN: 0218-1967
PURE UUID: b7b9366a-1c62-4bf8-8327-b3bc67b16f64
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Date deposited: 20 Jul 2015 09:54
Last modified: 15 Mar 2024 03:29
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