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For a positive integer  l  and a finite group  G , let, wheredenotes the set of non-monomial characters of  G . In this paper, we prove that if, then  G  is solvable. In particular, we show that for a non-solvable group  G , if, then  G  =  MC  is a central product of two subgroups  M  and  C  such thatand  G / M  is an  M -group. Among the other results, we arrive at the solvability of  G  by assuming.

The degrees of non-monomial characters and solvability of a finite group