Mathematical Research Letters

Volume 21 (2014)

Number 4

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

Pages: 649 – 661

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n4.a2

Authors

Yago Antolín (Department of Mathematics, Vanderbilt University, Nashville, Tennessee, U.S.A.)

Armando Martino (School of Mathematics, University of Southampton, United Kingdom)

Inga Schwabrow (School of Mathematics, United Kingdom)

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.

Keywords

free products, Kurosh rank, orderability, Bass-Serre theory

2010 Mathematics Subject Classification

Primary 20E06. Secondary 20E08.

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Published 27 October 2014