Finite quotients of braid groups

TL;DR

This paper establishes superexponential lower bounds on the sizes of finite non-cyclic quotients of braid groups and their commutator subgroups, advancing understanding of their algebraic structure.

Contribution

It provides new superexponential lower bounds on the sizes of finite quotients of braid groups and their commutator subgroups, which was previously unknown.

Findings

Superexponential lower bounds for finite non-cyclic quotients of braid groups

Similar bounds for nontrivial quotients of the commutator subgroup

Enhanced understanding of the algebraic complexity of braid groups

Abstract

We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the braid group.