Hokkaido Mathematical Journal

Hokkaido Mathematical Journal, 41 (2012) pp.185-208

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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]2d ≤ pn, where d is the smallest integer not less than M/m.

MSC(Primary) 20C15 p-group, extension, irreducible induced character, faithful irreducible character