The Geometry of Point Reflections and Quasigroups

Yuri Movsisyan, Victor Pambuccian

Research output: Contribution to journalArticlepeer-review

Abstract

This is a survey of results from the rich theory of medial and more general quasigroups and its close connection with the geometry of point-reflections. The emphasis is on questions regarding the simplest axiomatization, in the sense of the minimal number of variables appearing in the identtties, on dependence or independence of axioms, and on representation theorems in the style of Toyoda.

Original languageEnglish (US)
Article number132
JournalResults in Mathematics
Volume75
Issue number4
DOIs
StatePublished - Dec 1 2020

Keywords

  • Point-reflections
  • left Bruck loop
  • medial property
  • moufang loop
  • quasigroup
  • simple axiomatization

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

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