Superexponential distortion of free groups in virtually special Groups

Pratit Goswami; Maya Verma

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arXiv · 2508.18223

Superexponential distortion of free groups in virtually special Groups

Pratit Goswami·Maya Verma

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Abstract

For all integers $k, m > 0$, we construct a virtually special group $G$ containing a finite rank free subgroup $F$ whose distortion function in $G$ grows like $\exp^k(x^m)$. We also construct examples of virtually special groups containing finite rank free subgroups whose distortion functions grow bigger than any iterated exponential.

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Pratit Goswami, Maya Verma. 2025-08-25. Superexponential distortion of free groups in virtually special Groups. https://arxiv.org/abs/2508.18223

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