عنوان مقاله [English]
Let X be an irreducible character of a non-abelian group G. For non-negative integers n, m such that m+n>0 , we study the case when all the irreducible constituents of XnXm are linear. Mann proved that if G is a finite non-abelian group with an irreducible character X such that all the irreducible constituents of
X2 are linear, then G<Z(G) and as a consequence G is nilpotent. In this paper we generalize the result of Mann and prove that if m, n are non-negative integers with m+n>0 , and if X is an irreducible character of G, then all the irreducible constituents of XnXm are linear if and only if G<Z(G).