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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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the lower bounded of metrics on a group

Let $G$ be a finitely generated group, S is a set of generators. If $\forall s\in S, n\in \mathbb{Z}$, $\exists C>0$ such that $|s^n|_S\ge C|n|$, does it imply $\forall$ infinite order element $g\in G …
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