2014/05/06 by Oleg Viro, Viro, Oleg · 1 citation
Social Sciences · #22E67 #22E99 #51F15 #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Reflective Practices in Education
paper · pdf · doi:10.48550/arxiv.1405.1460
openalex publication_date 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and relations closely related to geometry. They allow to make fast and efficient geometric calculations. In this paper simple presentations of the isometry groups of Euclidean plane, 2-sphere, the real projective plane and groups SO(3), O(n) are introduced.