Chillag has showed that there is a single generalization showing that the sums of ordinary character tables, Brauer character, and projective indecomposable characters are positive integers. We show that Chillag's construction also applies to Isaacs' $\pi$-partial characters. We show that if an extra condition is assumed, then we can obtain upper and lower bounds on the Chillag's table sums. We will demonstrate that this condition holds for Brauer characters, $\pi$-partial characters, and projective indecomposable characters, and so we obtain upper and lower bounds for the table sums in those cases. We also obtain results regarding the sums of rows and columns in these tables.

Upper and lower bounds on Chillag table sums

The aim of this note is to characterize some quantitative properties in a finite group by using modular representation theoryUtilizing the Schur-Zassenhaus theorem and modular representation theory,the authors prove in this note that any prime p does not divide the number of p-regular elements of a finite groupAccording to the Brauer character table of a finite group,some information on number theory can be obtainedUsing modular representation theory and Galois theory,the authors present in this note that every row sum in the Brauer character table of any finite group is a rational integerIn addition,if a finite group is p-solvable,then each column sum in its Brauer character table is a rational integer

Two Properties of Brauer Character Tables

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Two Properties of Brauer Character Tables