PreprintCC BY-SA 4.0arXiv
Two problems about bases and independent sets in free groups
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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BibTeX
@misc{kochhyde2026problems,
title = {{Two problems about bases and independent sets in free groups}},
author = {Lucy Koch-Hyde and Éamonn Olive},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00382},
eprint = {2609.00382},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00382},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Two problems about bases and independent sets in free groups
AU - Lucy Koch-Hyde
AU - Éamonn Olive
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.00382
UR - https://arxiv.org/abs/2609.00382
AB - 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.
ER -