## Hokkaido Mathematical Journal

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

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

#### Abstract

For a prime *p*, we denote by *B*_{n} the cyclic group of order *p*^{n}. Let ϕ be a faithful irreducible character of *B*_{n}, where *p* is an odd prime. We study the *p*-group *G* containing *B*_{n} such that the induced character ϕ^{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} ≤ *p*^{n}, 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