A TECHNIQUE FOR THE SEARCH FOR VERTICES OF THE COMPONENTS OF A kG-PERMUTATION MODULE

摘要

In this paper we present a necessary condition for a p-group V <= G to be a vertex of some indecomposable direct summand of the permutation module k(H)up arrow(G), where H <= G, and G is a finite group. We call this condition H-suitability and present a method how to check for it. In an example, we determine all H-suitable groups. In fact, in this example every H-suitable group is the vertex of some indecomposable direct summand of k(H)up arrow(G).