On a Quasi-Phan Theorem for Orthogonal Groups

TL;DR

This paper presents a shorter, more efficient presentation of orthogonal groups by constructing an amalgam that refines previous work, contributing to the understanding of their algebraic structure.

Contribution

It introduces a more concise presentation of orthogonal groups, improving upon existing amalgam constructions by Gramlich and Van Maldeghem.

Findings

A new, shorter amalgam for orthogonal groups

Enhanced understanding of orthogonal group presentations

Comparison showing improved efficiency over prior work

Abstract

This paper constructs a presentation for the orthogonal groups. The amalgam is contained in that constructed by Ralf Gramlich Hendrik Van Maldeghem and arXiv:0708.1583 but it's shorter.