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The group of endotrivial modules for the symmetric and alternating groups.

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<mark>Journal publication date</mark>02/2010
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Issue number1
Number of pages13
Pages (from-to)83-95
Publication StatusPublished
<mark>Original language</mark>English


We complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n ≥ p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelian of rank 1 if n ≥ p2 + p and has rank 2 if p2 ≤ n < p2 + p. This completes the work begun earlier by Carlson, Mazza and Nakano.

Bibliographic note

http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 53 (1), pp 83-95 2010, © 2010 Cambridge University Press.