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arXiv · 2609.00382

Two problems about bases and independent sets in free groups

Lucy Koch-Hyde·Éamonn Olive
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Abstract

We will answer a problem of Dotsenko that asks for a tight upper bound on the rank of subgroups given a maximum length for its generators. Then, we will use the same tools to answer a longstanding problem of Grigorchuk in the 10th edition of the Kourovka notebook. We accomplish this using Stallings foldings and simple graph theory.

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Lucy Koch-Hyde, Éamonn Olive. 2026-08-31. Two problems about bases and independent sets in free groups. https://arxiv.org/abs/2609.00382

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