Vol. 14, No. 5, 2021

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Upper bounds for totally symmetric sets

Kevin Kordek, Lily Qiao Li and Caleb Partin

Vol. 14 (2021), No. 5, 853–870
Abstract

Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. 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 free product of solvable groups must have cyclic image.

Keywords
totally symmetric sets, homomorphisms, braid groups
Mathematical Subject Classification
Primary: 20E34, 20F65
Milestones
Received: 4 March 2021
Revised: 2 June 2021
Accepted: 4 July 2021
Published: 9 February 2022

Communicated by Kenneth S. Berenhaut
Authors
Kevin Kordek
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Lily Qiao Li
Department of Mathematics
University of California
Berkeley, CA
United States
Caleb Partin
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States