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Weights for 𝜋-partial characters of 𝜋-separable groups

  • Xuewu Chang EMAIL logo und Ping Jin
Veröffentlicht/Copyright: 7. November 2024

Abstract

The aim of this paper is to confirm a conjecture of Isaacs and Navarro from 1995, which asserts that, for any π -subgroup 𝑄 of a 𝜋-separable group 𝐺, the number of π -weights of 𝐺 with 𝑄 as the first component is larger than or equal to the number of irreducible 𝜋-partial characters of 𝐺 with 𝑄 as their vertex. We also give a sufficient condition to guarantee that these two numbers are equal, and thereby strengthen their main theorem on the 𝜋-version of the Alperin weight conjecture.

Award Identifier / Grant number: 12171289

Funding statement: This work was supported by the NSF of China (12171289) and by Fundamental Research Programs of Shanxi Province (20210302123429 and 20210302124077).

Acknowledgements

The authors are grateful to the referee for valuable comments and suggestions that greatly helped us to improve the presentation of this paper.

  1. Communicated by: Hung Tong-Viet

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Received: 2024-05-23
Revised: 2024-09-30
Published Online: 2024-11-07
Published in Print: 2025-05-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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