Spherically orderable groups

TL;DR

This paper introduces the concept of spherically ordered groups, explores their spectral properties, and determines the spectra for various natural groups, expanding the understanding of orderability in group theory.

Contribution

It defines spherically ordered groups and their spectra, providing new insights and calculations for these structures in group theory.

Findings

Spectra of spherical orderability are computed for several natural groups.

The notion of spherical orderability extends classical orderability concepts.

New classifications of groups based on spherical orderability are proposed.

Abstract

We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.