A Technique for the Search for Vertices of the Components of a kG-Permutation Module

Abstract

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  ↑ ^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  ↑ ^G .

Key Words:

• Group theory
• Representation theory

2010 Mathematics Subject Classification:

• 20C40
• 20G40

ACKNOWLEDGMENTS

I wish to express my deep gratitude to my supervisor John Murray for his constant help and valuable guidance.

Notes

Communicated by P. Tiep.