PreprintarXiv licencearXiv
The spectrum of conjugator length functions
Abstract
A recent program tries to find which functions appear as conjugator length functions. In this note, we show that any (computable) increasing function larger than n appears as ClG for some finitely generated (recursively presented) group. On the other hand, we demonstrate that either ClG must be constant or ClG(n)≻ n. Combining these, we obtain a complete description of which functions appear as conjugator length functions of finitely generated groups.
Related
BibTeX
@misc{vandeputte2026spectrum,
title = {{The spectrum of conjugator length functions}},
author = {Lukas Vandeputte},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09968},
eprint = {2609.09968},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09968},
}
RIS
TY - UNPB
TI - The spectrum of conjugator length functions
AU - Lukas Vandeputte
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09968
UR - https://arxiv.org/abs/2609.09968
AB - A recent program tries to find which functions appear as conjugator length functions. In this note, we show that any (computable) increasing function larger than n appears as Cl_G for some finitely generated (recursively presented) group. On the other hand, we demonstrate that either Cl_G must be constant or Cl_G(n)≻ n. Combining these, we obtain a complete description of which functions appear as conjugator length functions of finitely generated groups.
ER -