Short Presentations for Aut$_n^+$ and Out$_n^+$

TL;DR

This paper provides concise presentations for the special automorphism and outer automorphism groups of free groups using methods from a prior work, aiding in understanding their algebraic structure.

Contribution

It introduces short presentations for Aut$^+(F_n)$ and Out$^+(F_n)$ using established methods, simplifying their algebraic descriptions.

Findings

Short presentations for Aut$^+(F_n)$ and Out$^+(F_n)$ are obtained.

The methods from arXiv:0804.1396 are effectively applied.

The results facilitate further algebraic and computational studies.

Abstract

This paper uses the methods from arXiv:0804.1396 to give 'short' presentations for Aut$^+(F_n)$, the special automorphism group of the free group of rank $n$, and Out $^+(F_n)$ the special outer automorphism group of the free group of rank $n$.