论文标题
有限群体的平均角色程度和Gluck的猜想
The average character degree of finite groups and Gluck's conjecture
论文作者
论文摘要
我们证明，有限的组$ g $与琐碎的可解决的激进主义者的订单以$ {\ rm acd}（g）$（$ {\ rm acd}（g）$（不可约性字符的平均程度）限制。上面的拟合子组的索引是按照$ {\ rm acd}（g）$界定的，但是我们表明，在某些情况下，它是根据$ g $的不可约性字符的程度界定的，而$ g $的不可减少字符，而$ g $的不可约束，这些字符属于拟合子组的线性字符上。这使我们提出了Gluck猜想的精致版本。
We prove that the order of a finite group $G$ with trivial solvable radical is bounded above in terms of ${\rm acd}(G)$, the average degree of the irreducible characters. It is not true that the index of the Fitting subgroup is bounded above in terms of ${\rm acd}(G)$, but we show that in certain cases it is bounded in terms of the degrees of the irreducible characters of $G$ that lie over a linear character of the Fitting subgroup. This leads us to propose a refined version of Gluck's conjecture.
