When is a Bol loop Moufang?

TL;DR

This paper investigates conditions under which Bol loops are necessarily Moufang loops, demonstrating that certain identities or sets of equations can enforce the Moufang property.

Contribution

It introduces new criteria involving multiple identities or equations that guarantee a Bol loop is Moufang, extending previous understanding.

Findings

Multiple identities can force a Bol loop to be Moufang

Single identities may not be sufficient for this implication

Providing elements with choices of equations can ensure Moufang property

Abstract

There are a number of identities which, if satisfied by a Bol loop, imply that the loop is actually Moufang. In this paper we show that in a number of cases, the Moufang identity is also forced not by a single identity, but by giving elements a choice of equations to satisfy.