On Groups $G_{n}^{2}$ and Coxeter Groups
Vassily Olegovich Manturov

TL;DR
This paper proves that the group of free n-strand braids, $G_{n}^{2}$, is isomorphic to a subgroup of a semidirect product involving a specific Coxeter group and the symmetric group, revealing new structural insights.
Contribution
It establishes an isomorphism between $G_{n}^{2}$ and a subgroup of a semidirect product with a Coxeter group, linking braid groups to Coxeter group structures.
Findings
$G_{n}^{2}$ is isomorphic to a subgroup of a semidirect product involving $C(n,2)$ and $S_{n}$
Provides a new structural understanding of free braid groups
Connects braid groups with Coxeter group theory
Abstract
In the present paper, we prove that the group of free -strand braids is isomorphic to a subgroup of a semidirect product of some Coxeter group that we denote by and the symmetric group .
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