Upper and Lower Bounds of Table Sums

Abstract

For a group [Formula: see text], we produce upper and lower bounds for the sum of the entries of the Brauer character table of [Formula: see text] and the projective indecomposable character table of [Formula: see text]. When [Formula: see text] is a [Formula: see text]-separable group, we show that the sum of the entries in the table of Isaacs' partial characters is a real number, and we obtain upper and lower bounds for this sum.