Upper Bounds for Totally Symmetric Sets
Group Theory
2022-03-09 v1 Geometric Topology
Abstract
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a consequence, we derive restrictions on possible homomorphisms between these groups. One sample application of our results is that any homomorphism of a braid group to a direct product of solvable groups must have cyclic image.
Cite
@article{arxiv.2102.06270,
title = {Upper Bounds for Totally Symmetric Sets},
author = {Kevin Kordek and Qiao Li and Caleb Partin},
journal= {arXiv preprint arXiv:2102.06270},
year = {2022}
}
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11 pages