Weights for $\pi$-partial characters of $\pi$-separable groups

Xuewu Chang; Ping Jin

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arXiv · 2404.14125

Weights for $\pi$-partial characters of $\pi$-separable groups

Xuewu Chang·Ping Jin

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Abstract

The aim of this paper is to confirm an inequality predicted by Isaacs and Navarro in 1995, which asserts that for any $\pi'$-subgroup $Q$ of a $\pi$-separable group $G$, the number of $\pi'$-weights of $G$ with $Q$ as the first component always exceeds that of irreducible $\pi$-partial characters of $G$ with $Q$ as their vertex. We also give some sufficient condition to guarantee that these two numbers are equal, and thereby strengthen their main theorem on the $\pi$-version of the Alperin weight conjecture.

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Xuewu Chang, Ping Jin. 2024-04-22. Weights for $\pi$-partial characters of $\pi$-separable groups. https://arxiv.org/abs/2404.14125

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