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# 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: http://dx.doi.org/10.4310/MRL.2014.v21.n4.a2

#### Authors

#### 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.