Multiplication formulas in Moufang loops

TL;DR

This paper explores multiplication formulas in Moufang loops using groups with triality, constructs extensions of abelian groups, and analyzes minimal extensions of finite simple Moufang loops, advancing understanding of their algebraic structure.

Contribution

It introduces new multiplication formulas in Moufang loops and constructs their extensions, providing insights into their structure and minimal extensions.

Findings

Derived general multiplication formulas for Moufang loops

Constructed Moufang extensions of abelian groups

Described minimal extensions of finite simple Moufang loops

Abstract

Using groups with triality we obtain some general multiplication formulas in Moufang loops, construct Moufang extensions of abelian groups, and describe the structure of minimal extensions for finite simple Moufang loops over abelian groups.