Upper and Lower Bounds of Table Sums

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For a group G,we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G.When G is a π-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.
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