Classifying endotrivial $ kG $-modules, ie, elements of the Picard group of the stable module
category for an arbitrary finite group $ G $, has been a long-running quest. By deep work of …

This survey provides an overview of numerous results on p-permutation modules and the
closely related classes of endo-trivial, endo-permutation and endo-p-permutation modules …

We define the central concepts of this book. Namely the endotrivial and endo-permutation
modules, and the group of endotrivial modules. We present the subject following the …

Let G be a finite group and let T (G) be the abelian group of equivalence classes of
endotrivial k G-modules, where k is an algebraically closed field of characteristic p. We …

We determine the group of endotrivial modules (as an abstract group) for G a (quasi) simple
group of sporadic type, extending previous results in the literature. In many sporadic cases …

We examine how, in prime characteristic p, the group of endotrivial modules of a finite group
G and the group of endotrivial modules of a quotient of G modulo a normal subgroup of …

We provide a description of the torsion subgroup 𝑇𝑇⁢(G) of the finitely generated abelian
group T⁢(G) of endo-trivial kG-modules in the case that G has a dihedral Sylow 2-subgroup …

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 Thévenaz …