Abstract
Abstract The aim of this paper is to confirm a conjecture of Isaacs and Navarro from 1995, which asserts that, for any π ′ \pi^{\prime} -subgroup 𝑄 of a 𝜋-separable group 𝐺, the number of π ′ \pi^{\prime} -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.
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