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Endotrivial modules for the symmetric and alternating groups.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>02/2009
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Issue number1
Number of pages22
Pages (from-to)45-66
Publication StatusPublished
<mark>Original language</mark>English


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.

Bibliographic note

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.