Linear quasigroups. II

TL;DR

This paper continues the exploration of linear quasigroups, focusing on identities, linearity, and their relation to loops, while providing historical context and development of the theory.

Contribution

It introduces methods for deriving quasigroup identities from loop varieties and extends the understanding of linear quasigroups and their generalizations.

Findings

Identifies key identities and linearity conditions for quasigroups.

Connects quasigroup identities with loop theory.

Provides historical overview of quasigroup development.

Abstract

The article is a continuation of the author's work "Linear quasigroups. I" and devoted to linear quasigroups and some of their generalizations. In the second part identities and linearity of quasigroups are investigated, in particular, the approach of finding quasigroup identities from some variety of loops is presented. Besides that we give short chronology of development the theory of quasigroups and loops and some historical aspects.