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.
http://journals.cambridge.org/action/displayJournal?jid=UHY The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, © Cambridge University Press.