, Volume 94, Issue 1, pp 33-43

Subgroups of Free Groups: a Contribution to the Hanna Neumann Conjecture

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Abstract

We prove that the strengthened Hanna Neumann conjecture, on the rank of the inter-section of finitely generated subgroups of a free group, holds for a large class of groups characterized by geometric properties. One particular case of our result implies that the conjecture holds for all positively finitely generated subgroups of the free group F(A) (over the basis A), that is, for subgroups which admit a finite set of generators taken in the free monoid over A.