Invariants of Classical Braids Valued in $G_{n}^{2}$

TL;DR

This paper constructs invariants for the Artin braid group using groups $G_{n}^{2}$, which are simpler and have a solved word problem, and explores related groups $G_{n}^{3}$.

Contribution

It introduces new invariants of the braid group valued in $G_{n}^{2}$ and investigates properties of groups related to $G_{n}^{3}$.

Findings

Invariants of the braid group are constructed using $G_{n}^{2}$.

The word problem is solved in $G_{n}^{2}$ groups.

Groups related to $G_{n}^{3}$ are studied.

Abstract

The aim of the present note is to construct invariants of the Artin braid group valued in $G_{N}^{2}$, and further study of groups related to $G_{n}^{3}$. In the groups $G_{n}^{2}$, the word problem is solved; these groups are much simpler than $G_{n}^{3}$.