Brauer trees for blocks of cyclic defect in the groups \(G_ 2(q)\) for primes dividing \(q^ 2\pm q+1\)
type: Item
instance of: scholarly article
title: Brauer trees for blocks of cyclic defect in the groups \(G_ 2(q)\) for primes dividing \(q^ 2\pm q+1\)
zbMATH Open document ID: 0674.20004
DOI: 10.1016/0021-8693(89)90052-5
author: Josephine Shamash
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let \(G_ 2(q)\) be the finite Chevalley group of type \(G_ 2\) over the field with q elements (q a prime power not divisible by 2 and 3) of order \(q^ 6(q+1)^ 2(q-1)^ 2(q^ 2+q+1)(q^ 2-q+1)\). In this paper the author gives the distribution of the ordinary irreducible characters of \(G_ 2(q)\) into the p-blocks for the primes \(p\neq 2,3\) dividing \(q^ 2\pm q+1\). Furthermore the decomposition matrices of the p-blocks of cyclic defect are determined and described in form of their Brauer trees.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 4103327
zbMATH Keywords: finite Chevalley group
zbMATH Keywords: irreducible characters
zbMATH Keywords: p-blocks
zbMATH Keywords: decomposition matrices
zbMATH Keywords: cyclic defect
zbMATH Keywords: Brauer trees
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90052-5
OpenAlex ID: W2046638365
cites work: Q3682663
cites work: The conjugate classes of Chevalley groups of type \((G_2)\)
cites work: Q4073555
cites work: Q3955560
cites work: On the decomposition numbers of \(G_ 2(q)\)
cites work: On Some Simple Groups Defined by C. Chevalley
cites work: Blocks and brauer trees in the groupsG2(q) for primes dividingq±1
description: scientific article; zbMATH DE number 4103327