Weights for $Ï$-partial characters of $Ï$-separable groups

Xuewu Chang; Ping Jin

paper

Weights for $I ¨ $ -partial characters of $I ¨ $ -separable groups

arXiv:2404.14125

Abstract

The aim of this paper is to confirm an inequality predicted by Isaacs and Navarro in 1995, which asserts that for any $I ¨ ^{'}$ -subgroup $Q$ of a $I ¨ $ -separable group $G$ , the number of $I ¨ ^{'}$ -weights of $G$ with $Q$ as the first component always exceeds that of irreducible $I ¨ $ -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 $I ¨ $ -version of the Alperin weight conjecture.

Weights for I¨-partial characters of I¨-separable groups

Abstract

Weights for $I ¨ $ -partial characters of $I ¨ $ -separable groups