On saturated fusion systems and Brauer indecomposability of Scott modules

Radha Kessar, Naoko Kunugi, Naofumi Mitsuhashi

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let p be a prime number, G a finite group, P a p-subgroup of G and k an algebraically closed field of characteristic p. We study the relationship between the category FP(G) and the behavior of p-permutation kG-modules with vertex P under the Brauer construction. We give a sufficient condition for FP(G) to be a saturated fusion system. We prove that for Scott modules with abelian vertex, our condition is also necessary. In order to obtain our results, we give a criterion for the categories arising from the data of (b,G)-Brauer pairs in the sense of Alperin–Broué and Broué–Puig to be saturated fusion systems on the underlying p-group.
Original languageEnglish
Pages (from-to)90-103
Number of pages14
JournalJournal of Algebra
Volume340
Issue number1
Early online date8 Jun 2011
DOIs
Publication statusPublished - 15 Aug 2011

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Fusion
Module
P-groups
Vertex of a graph
Prime number
Algebraically closed
Permutation
Finite Group
Subgroup
Necessary
Sufficient Conditions
Relationships

Keywords

  • representations of finite groups
  • fusion systems
  • saturated triples
  • Scott modules

Cite this

On saturated fusion systems and Brauer indecomposability of Scott modules. / Kessar, Radha; Kunugi, Naoko ; Mitsuhashi, Naofumi.

In: Journal of Algebra, Vol. 340, No. 1, 15.08.2011, p. 90-103.

Research output: Contribution to journalArticle

Kessar, Radha ; Kunugi, Naoko ; Mitsuhashi, Naofumi. / On saturated fusion systems and Brauer indecomposability of Scott modules. In: Journal of Algebra. 2011 ; Vol. 340, No. 1. pp. 90-103.
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