12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > The group of endotrivial modules for the symmet...
View graph of relations

« Back

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

Research output: Contribution to journalJournal article

Published

Journal publication date02/2010
JournalProceedings of the Edinburgh Mathematical Society
Journal number1
Volume53
Number of pages13
Pages83-95
Original languageEnglish

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.

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.