Mathematical Research Letters
Volume 21 (2014)
Kurosh rank of intersections of subgroups of free products of right-orderable groups
Pages: 649 – 661
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.
free products, Kurosh rank, orderability, Bass-Serre theory
2010 Mathematics Subject Classification
Primary 20E06. Secondary 20E08.