Stable Torsion Length
Abstract
The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic groups. We then give a linear programming algorithm to compute a lower bound for stable torsion length in free products of groups. Moreover, we obtain an algorithm that exactly computes stable torsion length in free products of finite groups. The nature of the algorithm shows that stable torsion length is rational in this case. As applications, we give the first exact computations of stable torsion length for nontrivial examples.
Cite
@article{arxiv.2103.14116,
title = {Stable Torsion Length},
author = {Chloe I. Avery and Lvzhou Chen},
journal= {arXiv preprint arXiv:2103.14116},
year = {2022}
}
Comments
v2: strengthened the Rationality Theorem so that it holds for free products of arbitrary finite groups, revised based on the suggestions from referees; 39 pages, 14 figures