Is the intersection of two subgroups, defined below, always trivial? – mathoverflow.net

Is the intersection of two subgroups, defined below, always trivial? – mathoverflow.net

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Suppose, $G = \mathbb{Z} \ast H$, where $H$ is an arbitrary group. Suppose, $g \in G$ and $g \notin \langle\langle H \rangle \rangle $. Is $\langle\langle g \rangle \rangle \cap H$ always trivial? ...

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