On Rank of the Join of Two Subgroups in a Free Group
نویسنده
چکیده
Let H,K be two finitely generated subgroups of a free group, let 〈H,K〉 denote the subgroup generated by H,K, called the join of H,K, and let neither of H, K have finite index in 〈H,K〉. We prove the existence of an epimorphism ζ : 〈H,K〉 → F2, where F2 is a free group of rank 2, such that the restriction of ζ on both H and K is injective and the restriction ζ0 : H ∩K → ζ(H)∩ ζ(K) of ζ on H ∩K to ζ(H)∩ ζ(K) is surjective. This is obtained as a corollary of an analogous result on rank of the generalized join of two finitely generated subgroups in a free group.
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