On the length of the shortest non-trivial element in the derived and the lower central series

Abdelrhman Elkasapy; Andreas Thom

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arXiv · 1311.0138

On the length of the shortest non-trivial element in the derived and the lower central series

Abdelrhman Elkasapy·Andreas Thom

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Abstract

We provide upper and lower bounds on the length of the shortest non-trivial element in the derived series and lower central series in the free group on two generators. The techniques are used to provide new estimates on the nilpotent residual finiteness growth and on almost laws for compact groups.

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Abdelrhman Elkasapy, Andreas Thom. 2013-11-01. On the length of the shortest non-trivial element in the derived and the lower central series. https://arxiv.org/abs/1311.0138

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