Jon F. Carlson and Jacques The\'evenaz

Torsion endo-trivial modules

Abstract.
We prove that the group $T(G)$ of endo-trivial modules for a 
non-cyclic finite $p$-group $G$ is detected on restriction to 
the family of subgroups which are either elementary abelian
of rank 2 or (almost) extraspecial. This result is closely
related to the problem of finding the torsion subgroup of
$T(G)$. We give the complete structure of $T(G)$ when $G$
is dihedral, semi-dihedral, or quaternion.