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arXiv · 1509.04449

The Hanna Neumann Conjecture and the rank of the join

Joshua E. Hunt
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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.

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Joshua E. Hunt. 2015-09-15. The Hanna Neumann Conjecture and the rank of the join. https://arxiv.org/abs/1509.04449

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