On linear groups with a cyclic or T.I. Sylow subgroup
type: Item
instance of: scholarly article
title: On linear groups with a cyclic or T.I. Sylow subgroup
zbMATH Open document ID: 0638.20014
DOI: 10.1016/0021-8693(88)90296-7
author: Harvey I. Blau
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let G be a finite group with cyclic Sylow p-subgroup P. Let \(\chi\) be a faithful character of G. The author shows that if \(| P| >p\) and G is not p-solvable then \(\chi\) (1)\(\geq | P| -2\). Suppose that P is cyclic. Then if G is still not p-solvable \(\chi\) (1)\(\geq | P| -1\) and G/Z(G) is more or less alternating or special linear or projective special linear. If \(\chi\) is faithful and G is p-solvable then \(\chi\) (1) is almost as big as \([P:O_ p(G)]\) depending on the largest of the defect groups of the irreducible constituents of \(\chi\). If instead of cyclic P is T.I. and \(\chi (1)<| P| -1\) the \(O^{p'}(G)\) mod its center is usually in another list the author gives.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 4040163
zbMATH Keywords: T.I. Sylow subgroup
zbMATH Keywords: cyclic Sylow p-subgroup
zbMATH Keywords: faithful character
zbMATH Keywords: projective special linear
zbMATH Keywords: p-solvable
zbMATH Keywords: defect groups
describes a project that uses: CAS
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90296-7
OpenAlex ID: W1992272104
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description: scientific article; zbMATH DE number 4040163