具有两个特殊特征标维数的有限群

Finite Groups with Exactly Two Special Character Degrees

本文通过有限单群分类定理,首先证明了非交换单群S至少存在3个维数不同的不可约特征标χ,使得χ(1)2■|S|.设G为有限群,且只有两个不可约特征标χ满足χ(1)2■|G∶kerχ|,则G非单,进一步证明了G为可解群.

In this paper,by means of the classification theorem of finite simple groups,it is proved that there are at least three irreducible charactersχof nonabelian simple group S with different dimension which satisfy thatχ(1)2|S|.Let G be a finite group with two irreducible characters which satisfy thatχ(1)2|G∶kerχ|,then G is a non-simple group,and it is further proved that G is a solvable group.