Minimal modular character degrees for groups with a cyclic Sylow subgroup
type: Item
instance of: scholarly article
title: Minimal modular character degrees for groups with a cyclic Sylow subgroup
zbMATH Open document ID: 0696.20013
DOI: 10.1016/0021-8693(90)90167-M
author: Harvey I. Blau
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let F be a field of prime characteristic p, and let G be a finite linear group over F with a cyclic Sylow p-subgroup P such that \(| P| -1\) exceeds the degree of G. The main result of the paper under review shows that \(O^{p'}(G)O_{p'}(G)/O_{p'}(G)\) is isomorphic to either P, PSL(2,p), \(A_ 7\) \((p=7)\), \(J_ 1\) \((p=11)\), \(A_ 6\) \((p=5)\), \(A_ 7\) \((p=5)\), \(A_ p\), \(M_{11}\) \((p=11)\), \(M_{23}\) \((p=23)\), or PSL(n,q) where n is a prime not dividing q-1 \(and| P| =(q^ n-1)/(q-1)\). (The actual statement given in the paper is more precise.) This theorem extends earlier results by Brauer, Tuan, Feit, Ferguson and the author. Its proof makes use of the classification of finite simple groups. As an application the author classifies finite groups with a cyclic Sylow p- subgroup such that the projective cover of the trivial module in characteristic p has dimension p.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 4140020
zbMATH Keywords: finite linear group
zbMATH Keywords: cyclic Sylow p-subgroup
zbMATH Keywords: projective cover
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4140020