publication . Other literature type . 2012

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

SEKIGUCHI, Katsusuke;
Open Access English
  • Published: 01 Jun 2012
  • Publisher: Hokkaido University, Department of Mathematics
Abstract
For a prime p, we denote by B<sub>n</sub> the cyclic group of order p<sup>n</sup>. Let ϕ be a faithful irreducible character of B<sub>n</sub>, where p is an odd prime. We study the p-group G containing B<sub>n</sub> such that the induced character ϕ<sup>G</sup> is also irreducible. Set [N<sub>G</sub>(B<sub>n</sub>):B<sub>n</sub>] = p<sup>m</sup> and [G:B<sub>n</sub>] = p<sup>M</sup>. The purpose of this paper is to determine the structure of G under the hypothesis [N<sub>G</sub>(B<sub>n</sub>):B<sub>n</sub>]<sup>2d</sup> ≤ p<sup>n</sup>, where d is the smallest integer not less than M/m.
Subjects
ACM Computing Classification System: TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY
free text keywords: p-group, extension, irreducible induced character, faithful irreducible character, 20C15
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Other literature type . 2012
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