|
|||||
 |
|
|
|
|
|
|
|
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 |
|
