Extensions of cyclic \(p\)-groups which preserve the irreducibilities of induced characters.
type: Item
instance of: scholarly article
title: Extensions of cyclic \(p\)-groups which preserve the irreducibilities of induced characters.
zbMATH Open document ID: 1253.20006
author: Katsusuke Sekiguchi
published in: Hokkaido Mathematical Journal
publication date: 2012-06-29T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.hokmj/1340714412
review text: For a prime \(p\), denote by \(B_n\) the cyclic group of order \(p^n\). Let \(\varphi\) be a faithful irreducible character of \(B_n\), where \(p\) is an odd prime. In this paper \(p\)-groups \(G\) are studied containing \(B_n\) such that the induced character \(\varphi^G\) is also irreducible. Set \([N_G(B_n):B_n]=p^m\) and \([G:B_n]=p^M\). The purpose of this paper is to determine the structure of \(G\) under the hypothesis \([N_G(B_n):B_n]^{2d}\leq p^n\), where \(d\) is the smallest integer not less than \(M/m\). The author did succeed in doing so, thereby obtaining the structure for \(G\) explicitly.
reviewed by: Robert W. van der Waall
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 6051235
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: irreducibility of induced characters
zbMATH Keywords: M-groups
zbMATH Keywords: faithful characters
zbMATH Keywords: irreducible characters
MaRDI profile type: Publication
OpenAlex ID: W2050732336
DOI: 10.14492/HOKMJ/1340714412
description: scientific article; zbMATH DE number 6051235