Smallest nontrivial quotients of the commutator subgroup of braid groups

TL;DR

This paper proves that the smallest non-trivial quotients of the commutator subgroups of braid groups are the alternating groups, confirming a conjecture and characterizing minimal quotient maps.

Contribution

It establishes the minimal non-trivial quotients of braid group commutator subgroups as alternating groups and characterizes the minimal quotient maps.

Findings

Smallest non-trivial quotients are the alternating groups.

Any minimal quotient map is the standard projection composed with an automorphism.

Confirmed a conjecture of Chudnovsky-Kordek-Li-Partin.

Abstract

We prove that the smallest non-trivial quotients of the commutator subgroups of the braid groups are the alternating groups, proving a conjecture of Chudnovsky-Kordek-Li-Partin. Furthermore, we show that any minimal quotient map is the standard projection, composed with an automorphism of the alternating group.