Finite groups with almost distinct character degrees

David Chillag, Marcel Herzog

Research output: Contribution to journalArticlepeer-review

Abstract

Finite groups with the nonlinear irreducible characters of distinct degrees, were classified by the authors and Berkovich. These groups are clearly of even order. In groups of odd order, every irreducible character degree occurs at least twice. In this article we classify finite nonperfect groups G, such that χ (1) = θ (1) if and only if θ = over(χ, -) for any nonlinear χ ≠ θ ∈ Irr (G). We also present a description of finite groups in which x G ⊆ class (x) ∪ class (x-1) for every x ∈ G - G. These groups generalize the Frobenius groups with an abelian complement, and their description is needed for the proof of the above mentioned result on characters.

Original languageEnglish
Pages (from-to)716-729
Number of pages14
JournalJournal of Algebra
Volume319
Issue number2
DOIs
StatePublished - 15 Jan 2008

Keywords

  • Character degrees
  • Extended Camina pairs
  • Groups of odd order

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