特征标次数的重数与可解群结构

Multiplicity of Character Degrees and the Structure of Solvable Groups

非线性不可约特征标次数的重数全部为1的有限群的分类是熟知的.对可解群,本文讨论更一般的,即非线性不可约特征标次数的重数都与群阶互素的有限群的纯群论性质.特别地,得到了非线性不可约特征标次数的重数均小于2p的奇阶群G的分类结果.这里p为群阶|G|的最小素因子.

The classification of finite groups in which the multiplicity of each nonlinear irreducible character degree is equal to one is well known. For a solvable group G, we consider a more general case in this paper, namely the multiplicities of nonlinear irreducible character degrees of G are always co-prime to the group order |G|. In particular, we classify finite groups G of odd order in which the multiplicities of nonlinear irreducible character degrees are all less than 2p, where p is the minimal prune divisor of the group order |G|.