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Character triples and relative defect zero characters

  • Junwei Zhang , Lizhong Wang und Ping Jin EMAIL logo
Veröffentlicht/Copyright: 27. Februar 2025
Journal of Group Theory
Aus der Zeitschrift Journal of Group Theory Band 28 Heft 4

Abstract

Given a character triple ( G , N , θ ) , which means that 𝐺 is a finite group with N ⁢ ⊲ ⁢ G and θ ∈ Irr ⁡ ( N ) is 𝐺-invariant, we introduce the notion of a 𝜋-quasi-extension of 𝜃 to 𝐺, where 𝜋 is the set of primes dividing the order of the cohomology element [ θ ] G / N ∈ H 2 ⁢ ( G / N , C × ) associated with the character triple, and then we establish the uniqueness of such an extension in the normalized case. As an application, we use the 𝜋-quasi-extension of 𝜃 to construct a bijection from the set of 𝜋-defect zero characters of G / N onto the set of relative 𝜋-defect zero characters of 𝐺 over 𝜃. Our results generalize the related theorems of M. Murai and of G. Navarro.

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 12431001

Award Identifier / Grant number: 12171289

Funding statement: This work was supported by the NSF of China (Nos. 12431001, 12171289).

Acknowledgements

The authors are grateful to the referee for valuable comments and suggestions that greatly improve the exposition of the paper, and to Professor Jiping Zhang for his guidance and encouragement.

  1. Communicated by: Hung Tong-Viet

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Received: 2024-08-23
Revised: 2025-01-18
Published Online: 2025-02-27
Published in Print: 2025-07-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On the kernel of actions on asymptotic cones
  3. CAT(0) cube complexes and asymptotically rigid mapping class groups
  4. Iwip endomorphisms of free groups and fixed points of graph selfmaps
  5. Space of orders with finite Cantor–Bendixson rank
  6. Lifting subgroups of PSL2 to SL2 over local fields
  7. Regular 3-polytopes of order 2𝑛𝑝
  8. On the number of tuples of group elements satisfying a first-order formula
  9. Exponent-critical groups
  10. On soluble groups in which commutators have prime power order
  11. A character theoretic criterion for Fitting height
  12. Hilbert divisors and degrees of irreducible Brauer characters
  13. Character triples and relative defect zero characters
https://doi.org/10.1515/jgth-2024-0176

Artikel in diesem Heft

  1. Frontmatter
  2. On the kernel of actions on asymptotic cones
  3. CAT(0) cube complexes and asymptotically rigid mapping class groups
  4. Iwip endomorphisms of free groups and fixed points of graph selfmaps
  5. Space of orders with finite Cantor–Bendixson rank
  6. Lifting subgroups of PSL2 to SL2 over local fields
  7. Regular 3-polytopes of order 2𝑛𝑝
  8. On the number of tuples of group elements satisfying a first-order formula
  9. Exponent-critical groups
  10. On soluble groups in which commutators have prime power order
  11. A character theoretic criterion for Fitting height
  12. Hilbert divisors and degrees of irreducible Brauer characters
  13. Character triples and relative defect zero characters
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