Characterization of finite groups generated by reflections and rotations

TL;DR

This paper characterizes finite groups generated by reflections and rotations acting on Euclidean spaces, using the structure of the quotient space V/G to understand their properties.

Contribution

It provides a new characterization of such groups based on the quotient space structure, extending previous classifications.

Findings

Finite groups generated by reflections and rotations are characterized via their quotient space structure.

The quotient space V/G has a piecewise linear structure that reflects the group's properties.

The approach links geometric group actions with topological and combinatorial features.

Abstract

We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient piecewise linear structure.