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

Carlson, Jon and Hemmer, Dave and Mazza, Nadia (2010) The group of endotrivial modules for the symmetric and alternating groups. Proceedings of the Edinburgh Mathematical Society, 53 (1). pp. 83-95. ISSN 0013-0915

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    Abstract

    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.

    Item Type: Article
    Journal or Publication Title: Proceedings of the Edinburgh Mathematical Society
    Additional Information: 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.
    Uncontrolled Keywords: endotrivial module ; endopermutation module ; symmetric groups ; alternating groups
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 33519
    Deposited By: Mr Richard Ingham
    Deposited On: 26 May 2010 11:27
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 12:44
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/33519

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