On rank of the join of two subgroups in a free group
Autor: | Ivanov, Sergei V. |
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Rok vydání: | 2016 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | Let $H, K$ be two finitely generated subgroups of a free group, let $\langle H, K \rangle$ denote the subgroup generated by $H, K$, called the join of $H, K$, and let neither of $H$, $K$ have finite index in $\langle H, K \rangle$. We prove the existence of an epimorphism $\zeta : \langle H, K \rangle \to F_2$, where $F_2$ is a free group of rank 2, such that the restriction of $\zeta$ on both $H$ and $K$ is injective and the restriction $\zeta_0 : H \cap K \to \zeta (H) \cap \zeta (K) $ of $\zeta$ on $H \cap K $ to $\zeta (H) \cap \zeta (K)$ 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. Comment: 14 pages, 1 figure |
Databáze: | arXiv |
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