The Cartan matrix of a certain class of finite solvable groups
type: Item
instance of: scholarly article
title: The Cartan matrix of a certain class of finite solvable groups
zbMATH Open document ID: 0954.20006
author: Tomoyuki Wada
published in: Osaka Journal of Mathematics
publication date: 2001-02-08T00:00:00Z
review text: Let \(p\) and \(q\) be different primes, and let \(G\) be the group of affine semilinear transformations on the finite field with \(p^{pq}\) elements. The author computes the Cartan matrix of \(G\) in characteristic \(p\). He then uses this result in order to verify special cases of his conjecture that \(k(B)\), the number of irreducible characters in a \(p\)-block \(B\) of a \(p\)-solvable group, is bounded by \(\rho(B)\), the largest eigenvalue the Cartan matrix of \(B\).
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 1462593
zbMATH Keywords: defect groups
zbMATH Keywords: Perron-Frobenius eigenvalues
zbMATH Keywords: \(p\)-blocks
zbMATH Keywords: \(p\)-solvable groups
zbMATH Keywords: groups of affine semilinear transformations
zbMATH Keywords: finite fields
zbMATH Keywords: Cartan matrices
zbMATH Keywords: numbers of irreducible characters
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1462593