Automorphism groups of some pure braid groups

TL;DR

This paper determines finite presentations for the automorphism groups of certain pure braid groups, specifically those related to Artin and full monomial groups, advancing understanding of their algebraic structure.

Contribution

It provides explicit finite presentations for automorphism groups of specific pure braid groups, a novel result in the algebraic study of braid groups.

Findings

Finite presentations for automorphism groups of Artin pure braid groups.

Finite presentations for automorphism groups of pure braid groups related to full monomial groups.

Enhanced understanding of the automorphism structure of these braid groups.

Abstract

We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.