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 inX are connected. In particular, ifX is an l × l-matrix, A is an s × t-matrix, and, moreover, the squares A and C are opposite, thenr(A)=r(C) + s + t − l; here.r(M) is the rank of a matrix M. Associated with such each block ofX is some integral nonnegative parameter m, and we have m=0 iff A, B, C, and D are active fragments ofX. Supported by RFFR grant No. 96-01-00488. Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 273–279, May–June, 2000.