Hokkaido Mathematical Journal

Extensions of cyclic p-groups which preserve the irreducibilities of induced characters

Katsusuke SEKIGUCHI

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Abstract

For a prime p, we denote by Bn the cyclic group of order pn. Let ϕ be a faithful irreducible character of Bn, where p is an odd prime. We study the p-group G containing Bn such that the induced character ϕG is also irreducible. Set [NG(Bn):Bn] = pm and [G:Bn] = pM. The purpose of this paper is to determine the structure of G under the hypothesis [NG(Bn):Bn]2dpn, where d is the smallest integer not less than M/m.

Article information

Source
Hokkaido Math. J., Volume 41, Number 2 (2012), 185-208.

Dates
First available in Project Euclid: 26 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1340714412

Digital Object Identifier
doi:10.14492/hokmj/1340714412

Mathematical Reviews number (MathSciNet)
MR2977044

Zentralblatt MATH identifier
1253.20006

Subjects
Primary: 20C15: Ordinary representations and characters

Keywords
p-group extension irreducible induced character faithful irreducible character

Citation

SEKIGUCHI, Katsusuke. Extensions of cyclic p -groups which preserve the irreducibilities of induced characters. Hokkaido Math. J. 41 (2012), no. 2, 185--208. doi:10.14492/hokmj/1340714412. https://projecteuclid.org/euclid.hokmj/1340714412


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