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Kurosh rank of intersections of subgroups of free products of right-orderable groups

Kurosh rank of intersections of subgroups of free products of right-orderable groups
Kurosh rank of intersections of subgroups of free products of right-orderable groups
We prove that the reduced Kurosh rank of the intersection of two subgroups H and K of a free product of right-orderable groups is bounded above by the product of the reduced Kurosh ranks of H and K.

In particular, taking the fundamental group of a graph of groups with trivial vertex and edge groups, and its Bass-Serre tree, our theorem becomes the desired inequality of the usual strengthened Hanna Neumann conjecture for free groups.
1073-2780
649-661
Antolin, Yago
2ff7c13c-8a0d-4a50-9de5-63a750896e4c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Schwabrow, Inga
9564385e-f4b2-4fef-99c4-3259203f3067
Antolin, Yago
2ff7c13c-8a0d-4a50-9de5-63a750896e4c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Schwabrow, Inga
9564385e-f4b2-4fef-99c4-3259203f3067

Antolin, Yago, Martino, Armando and Schwabrow, Inga (2014) Kurosh rank of intersections of subgroups of free products of right-orderable groups. Mathematical Research Letters, 21 (4), 649-661. (doi:10.4310/MRL.2014.v21.n4.a2).

Record type: Article

Abstract

We prove that the reduced Kurosh rank of the intersection of two subgroups H and K of a free product of right-orderable groups is bounded above by the product of the reduced Kurosh ranks of H and K.

In particular, taking the fundamental group of a graph of groups with trivial vertex and edge groups, and its Bass-Serre tree, our theorem becomes the desired inequality of the usual strengthened Hanna Neumann conjecture for free groups.

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Published date: 2014
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 402874
URI: http://eprints.soton.ac.uk/id/eprint/402874
DOI: doi:10.4310/MRL.2014.v21.n4.a2
ISSN: 1073-2780
PURE UUID: 1fe25c19-9675-47d9-b803-3fc01afcfd4e
ORCID for Armando Martino: ORCID iD orcid.org/0000-0002-5350-3029

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Date deposited: 17 Nov 2016 14:05
Last modified: 15 Mar 2024 03:32

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Contributors

Author: Yago Antolin
Author: Armando Martino ORCID iD
Author: Inga Schwabrow

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