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Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations

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An application of ping-pong lemma

Let $F_2$ be free group of rank two with generators $a$ and $b$. If $H$ is a subgroup of $F_2$ generated by $d\geq 2$ elements with $$H=\langle a,b^{-k}ab^k, k=1,2,...,d-1\rangle,$$ I was trying to us …