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

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 determin...

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Bibliographic Details
Published in:Communications in algebra 2015-02, Vol.43 (2), p.659-673
Main Author: Pforte, Lars
Format: Article
Language:English
Subjects:
Group theory
Representation theory
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Summary: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 .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.843326