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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Official URL: http://dx.doi.org/10.1017/S0013091508000618

## 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 |
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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: | 19 Oct 2017 03:07 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/33519 |

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