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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
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Abstract |
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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. |
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Keywords
totally symmetric sets, homomorphisms, braid groups
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Mathematical Subject Classification
Primary: 20E34, 20F65
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Milestones
Received: 4 March 2021
Revised: 2 June 2021
Accepted: 4 July 2021
Published: 9 February 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Kevin Kordek | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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| Lily Qiao Li | |
| Department of Mathematics University of California Berkeley, CA United States |
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| Caleb Partin | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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