Characters of subnormal subgroups of M-groups
type: Item
instance of: scholarly article
title: Characters of subnormal subgroups of M-groups
zbMATH Open document ID: 0538.20004
DOI: 10.1007/BF01194046
author: I. M. Isaacs
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: By definition, a finite group G is called an M-group if each of its irreducible complex characters is induced from a linear character of a subgroup of G. In this paper several theorems are proved. The most important are Theorem 1: Let G be an M-group and let S be a subnormal subgroup of odd index in G. Then every primitive character of S is linear. Theorem 2: Let G be an M-group, S a subnormal subgroup of G with \(| G:S|\) odd. Let \(\alpha \in Irr(S)\) be p-special for some prime p. Then \(\alpha\) is monomial. Theorem 1 follows from theorem 2 with the help of some lemmas and theorems also proved in this paper.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D35
zbMATH DE Number: 3855358
zbMATH Keywords: M-group
zbMATH Keywords: irreducible complex characters
zbMATH Keywords: linear character
zbMATH Keywords: subnormal subgroup
zbMATH Keywords: primitive character
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
cites work: A characteristic class of characters of finite \(\pi\)-separable groups
cites work: Q4103728
cites work: Primitive characters, normal subgroups, and M-groups
cites work: Characters of \(\pi\)-separable groups
cites work: Induction and Restriction of π-Special Characters
Recommended article: Q3491800
Recommended article: Q3829707
Recommended article: Q3686874
Recommended article: Characters of maximal subgroups of \(M\)-groups
Recommended article: Q5185238
Recommended article: Primitive characters of subgroups of M-groups
Recommended article: A subnormality criterion in finite groups related to character degrees
Recommended article: Primitive characters of subgroups of $M$-groups
Recommended article: Q4712576
Recommended article: Certain irreducible characters over a normal subgroup
description: scientific article; zbMATH DE number 3855358