Endotrivial modules for the symmetric and alternating groups
(to appear in the Proceedings of the Edinburgh Math. Soc.)

by Jon F. Carlson, Nadia Mazza and Daniel K. Nakano

In this paper we determine the group of endotrivial modules for
certain symmetric and alternating groups in characteristic $p$. If $p=2$,
then the group is generated by the class of $\Omega^n(k)$ except
in a few low degrees. If $p >2$, then the group is only determined for
degrees less than $p^2$. In these cases we show that there are several
Young modules which are endotrivial.