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

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

#### 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.

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Primary Subjects: 20C15