A PROPERTY OF THE CHARACTER TABLE FOR A FINITE GROUP

A character table X of a finite group is broken up into four squares: A. B. C, and D. We establish relations via which ranks of the matrices in X are connected. In particular, if X is an l x l-matrix, A is an s x t-matrix. and. moreover, the squares A and C are opposite, then r(A)A = r(C) +s+t- l; here. r(M) is the rank of a matrix M. Associated with such each block of X is some integral nonnegative parameter m, and we have m = 0 iff A, B, C, and D are active fragments of X.