The Hanna Neumann Conjecture and the rank of the join

Abstract

The Hanna Neumann conjecture gives a bound on the intersection of finitely generated subgroups of free groups. We explore a natural extension of this result, which turns out to be true only in the finite index case, and provide counterexamples for the general case. We also see that the graph-based method of generating random subgroups of free groups developed by Bassino, Nicaud and Weil is well-suited to generating subgroups with non-trivial intersections. The same method is then used to generate a counterexample to a similar conjecture of Guzman.

9 pages, 4 figures; added counterexample to a conjecture of Guzman

References in corpus (3)

• Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture
• Statistical properties of subgroups of free groups
• Graphs of subgroups of free groups