Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Endotrivial modules for the symmetric and alternating groups

Jon F. Carlsona1, Nadia Mazzaa2 and Daniel K. Nakanoa1

a1 Department of Mathematics, University of Georgia, Athens, GA 30602, USA (jfc@math.uga.edu; nakano@math.uga.edu)

a2 Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK

Abstract

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 Ωn(k) except in a few low degrees. If p > 2, then the group is only determined for degrees less than p2. In these cases we show that there are several Young modules which are endotrivial.

(Received September 15 2006)

Keywords

  • endotrivial modules;
  • Young modules;
  • symmetric groups;
  • alternating groups

2000 Mathematics subject classification

  • Primary 20C20;
  • 20C30