Mathematical logic, algebra and number theory

Spherically ordered groups

S. V. Sudoplatov

Sobolev Institute of Mathematics, Academician Koptyug avenue, 4 630090, Novosibirsk, Russia

Abstract: We introduce and study the class of spherically ordered groups. Axioms of spherical orders used for these groups are examined and their (in)dependence is shown. The notions of spherically orderable groups and their spectra of spherical orderability are defined. Values of these spectra are found for a series of certain groups.

Keywords: spherical order, group, spectrum of spherical orderability.

UDC: 510.67, 512.545

MSC: 03C62, 06F15, 05A05

Received July 19, 2024, published December 11, 2024

Language: English

DOI: 10.33048/semi.2024.21.084