A class of finite simple Bol loops of exponent 2

TL;DR

This paper introduces an infinite class of finite simple right Bol loops of exponent 2, with their right multiplication groups structured as extensions of elementary Abelian 2-groups by S_5, answering prior open questions.

Contribution

It constructs a new infinite class of finite simple Bol loops of exponent 2 with specific group extension properties, expanding understanding of Bol loop structures.

Findings

Infinite class of finite simple Bol loops of exponent 2

Right multiplication groups are extensions of elementary Abelian 2-groups by S_5

Addresses open questions posed by M. Aschbacher

Abstract

In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by $S_5$. The construction uses the description of the structure of such loops given by M. Aschbacher. These results answer some questions of M. Aschbacher.