Edge Inversions in $(P_k)$-closed Groups
Group Theory
2026-01-28 v1 Combinatorics
Abstract
We construct -closed groups acting on in which all edge inversions have infinite order. This provides a negative answer to a question posed by Tornier. We also construct a family of -closed groups for which the smallest order of an edge inversion is an arbitrarily high finite number.
Cite
@article{arxiv.2601.18982,
title = {Edge Inversions in $(P_k)$-closed Groups},
author = {Kirwin Hampshire and Florian Lehner and Andrew Wood},
journal= {arXiv preprint arXiv:2601.18982},
year = {2026}
}