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arXiv · 2011.04028

Linear time algorithm for the conjugacy problem in the first Grigorchuk group

Mitra Modi·Mathew Seedhom·Alexander Ushakov
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Abstract

We prove that the conjugacy problem in the first Grigorchuck group $\Gamma$ can be solved in linear time. Furthermore, the problem to decide if a list of elements $w_1,\ldots,w_k\in\Gamma$ contains a pair of conjugate elements can be solved in linear time. We also show that a conjugator for a pair of conjugate element $u,v\in\Gamma$ can be found in polynomial time.

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Mitra Modi, Mathew Seedhom, Alexander Ushakov. 2020-11-08. Linear time algorithm for the conjugacy problem in the first Grigorchuk group. https://arxiv.org/abs/2011.04028

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