关键词: 有限可解群, 指标阶图, 表示, 模

Abstract: It is proved that there exists no finite solvable group G with the following as its character degree graph: .____.____.____. . The result solves an important open problem by Huppert and provides more evidence supporting the well-known conjecture which claims that the diameter of the degree graph of any finite solvable group is at most 2.

Key words: finite solvable group, degree graph, representation, module