Cartan matrices for blocks of finite p-solvable groups with two simple modules
type: Item
instance of: scholarly article
title: Cartan matrices for blocks of finite p-solvable groups with two simple modules
zbMATH Open document ID: 0733.20001
DOI: 10.1016/0021-8693(91)90268-D
author: Yasushi Ninomiya
author: Tomoyuki Wada
published in: Journal of Algebra
publication date: 1991-01-01T00:00:00Z
review text: Let p be a prime, G a finite p-solvable group and B a p-block of G with exactly two simple modules M and N in characteristic p. The authors describe the Cartan matrix C of B in terms of its elementary divisors and of the dimensions of M and N. They are led to conjecture that the \(p'\)- parts of dim M and dim N coincide. This conjecture is proved in several cases. If the conjecture is true then C is determined by its elementary divisors and the orders of the vertices of M and N alone.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 4212295
zbMATH Keywords: defect group
zbMATH Keywords: principal block
zbMATH Keywords: finite p-solvable group
zbMATH Keywords: p-block
zbMATH Keywords: simple modules
zbMATH Keywords: Cartan matrix
zbMATH Keywords: elementary divisors
zbMATH Keywords: vertices
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4212295