On Twisted homogeneous racks of type D

TL;DR

This paper develops techniques to determine when twisted homogeneous racks of a certain class are of type D, applying these methods to cases involving alternating and sporadic groups.

Contribution

It introduces new techniques for identifying type D twisted homogeneous racks and applies them to specific classes of groups, including alternating and sporadic groups.

Findings

Techniques for checking type D in twisted homogeneous racks

Application to alternating groups for n≥5

Application to sporadic groups

Abstract

We develop some techniques to check when a twisted homogeneous rack of class (L,t,\theta) is of type D. Then we apply the obtained results to the cases L an alternating group on n letters, n\geq 5, or L a sporadic group.