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Codegrees and nilpotence class of p-groups

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Published/Copyright: December 17, 2015
Journal of Group Theory
From the journal Journal of Group Theory Volume 19 Issue 4

Abstract

If χ is an irreducible character of a finite group G, then the codegree of χ is |G:ker(χ)|/χ(1). We show that if G is a p-group, then the nilpotence class of G is bounded in terms of the largest codegree for an irreducible character of G.

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11171243

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11201385

Funding source: Natural Science Foundation of Fujian Province

Award Identifier / Grant number: 2015J01027

Funding statement: The first author is supported by the National Natural Science Foundation of China (No. 11171243, No. 11201385), the Natural Science Foundation of Fujian Province (No. 2015J01027).

The first author thanks China Scholarship Council (CSC) and the Department of Mathematical Sciences of Kent State University for its hospitality.

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Received: 2015-8-14
Revised: 2015-9-21
Published Online: 2015-12-17
Published in Print: 2016-7-1

© 2016 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Codegrees and nilpotence class of p-groups
  3. On finite 2-equilibrated p-groups
  4. Minimal dimension of faithful representations for p-groups
  5. On the Christensen–Wang bounds for the ghost number of a p-group algebra
  6. A family of non-Schurian p-Schur rings over groups of order p3
  7. Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
  8. Symmetric powers of Nat SL(2,𝕂)
  9. Nested GVZ-groups
  10. On some groups generated by involutions
  11. Thompson’s conjecture for finite simple groups of Lie type Bn and Cn
https://doi.org/10.1515/jgth-2015-0039

Articles in the same Issue

  1. Frontmatter
  2. Codegrees and nilpotence class of p-groups
  3. On finite 2-equilibrated p-groups
  4. Minimal dimension of faithful representations for p-groups
  5. On the Christensen–Wang bounds for the ghost number of a p-group algebra
  6. A family of non-Schurian p-Schur rings over groups of order p3
  7. Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
  8. Symmetric powers of Nat SL(2,𝕂)
  9. Nested GVZ-groups
  10. On some groups generated by involutions
  11. Thompson’s conjecture for finite simple groups of Lie type Bn and Cn
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