Trivial source endo-trivial modules for finite groups with a semi-dihedral Sylow $2$-subgroup

TL;DR

This paper completes the classification of endo-trivial modules for finite groups with semi-dihedral Sylow 2-subgroups, building on previous work by Carlson, Mazza, and Thévaz from 2013.

Contribution

It finalizes the classification of trivial source endo-trivial modules for groups with semi-dihedral Sylow 2-subgroups, extending prior research.

Findings

Complete classification of endo-trivial modules for semi-dihedral Sylow 2-subgroups

Identification of trivial source endo-trivial modules in this context

Extension of previous classification results

Abstract

We finish off the classification of the endo-trivial modules of finite groups with Sylow $2$-subgroups isomorphic to a semi-dihedral $2$-group started by Carlson, Mazza and Th\'evenaz in their article "Endotrivial modules over groups with quaternion or semi-dihedral Sylow $2$-subgroup" published in 2013.