On the Vertices of Simple Modules for Symmetric Groups

In this article, we are concerned with the computation of vertices of some series of simple modules for the symmetric group of n letters in odd characteristic. In the first, the second, and the third section of this work we recall some more or less general results that are needed in our proofs. The fourth section contains new ingredients (in terms of dimension) that play an important role in our proofs of the main results in the last section.