Irreducible characters of even degree and normal Sylow 2-subgroups
Irreducible characters of even degree and normal Sylow 2-subgroups
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DOI：
10.1017/s0305004116000669
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发表时间：
2016-06
影响因子：
0.8
通讯作者：
N. Hung;P. Tiep
中科院分区：
文献类型：
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作者：
N. Hung;P. Tiep
关于有限群的特征标度的经典Itô-Michler定理认为，如果有限群G的每个复不可约特征标的度与给定的素数p互质，则G有正规的Sylow p-子群。我们提出了一个新的方向来推广这个定理，通过引入一个关于特征标度的不变量。证明了若G的线性不可约特征标和偶次不可约特征标的平均度小于4/3，则G存在正规Sylow 2-子群，以及相应的实值特征标和强真实的特征标的类似物.这些结果改进了关于Ito-Michler定理的几个早期结果。
Abstract The classical Itô-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group G is coprime to a given prime p, then G has a normal Sylow p-subgroup. We propose a new direction to generalize this theorem by introducing an invariant concerning character degrees. We show that if the average degree of linear and even-degree irreducible characters of G is less than 4/3 then G has a normal Sylow 2-subgroup, as well as corresponding analogues for real-valued characters and strongly real characters. These results improve on several earlier results concerning the Itô-Michler theorem.