Irreducible constituents of induced monomial characters
type: Item
instance of: scholarly article
title: Irreducible constituents of induced monomial characters
zbMATH Open document ID: 0609.20004
DOI: 10.1016/0021-8693(87)90191-8
author: N. S. Hekster
author: Robert W. van der Waall
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The following two results are proved: Th. A. Let G be a p-solvable finite group with \(p>2\) and let \(N\trianglelefteq G\) with G/N supersolvable of odd order, \(\pi\) (\(| G/N|)\subseteq \pi (p(p-1))\). Suppose \(\theta\in Irr(N)\) is monomial and \(\theta\) (1) is a power of p. Then every irreducible constituent of \(\theta^ G\) is monomial. - Th. B. Let G be as in Th. A and suppose \(\chi\in Irr(G)\) is primitive and \(\chi\) (1) is a power of p. Let \(N\trianglelefteq G\) and G/N be as in Th. A. Then \(\chi_ N\) is irreducible and primitive. Both theorems are false if \(p=2\) or if \(p>2\) and \(| G/N|\) is even. Th. A is a converse to Dade's following theorem: Let G be p- solvable, \(p>2\), and suppose \(\chi\in Irr(G)\) is monomial and \(\chi\) (1) is a power of p. Let S be a subnormal subgroup of G. Then every irreducible constituent of \(\chi_ S\) is monomial.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3985484
zbMATH Keywords: p-solvable finite group
zbMATH Keywords: monomial
zbMATH Keywords: irreducible constituent
zbMATH Keywords: primitive
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90191-8
OpenAlex ID: W2063670448
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description: scientific article; zbMATH DE number 3985484