具有固定特征标次数的群：一般情形
Groups with a Fixed Character Degree: The General Case
AI总结：
该研究针对具有固定特征标次数的一般群，扩展了可解群存在阿贝尔π-子群的算术条件刻画，移除了特征标次数的无平方因子假设，还证明了阿贝尔π-子群对Fitting子群π'-部分的忠实作用可导出相同条件。
AI中文摘要：
我们得到了可解群存在阿贝尔π-子群时满足的算术条件。首先，我们移除了部分固定不可约特征标次数的无平方因子假设，扩展了此前的刻画。随后，我们证明当π为前述特征标次数的素因子集合时，阿贝尔π-子群对Fitting子群的π'-部分的忠实作用也会导出相同的算术条件。
英文摘要：
We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $π$-subgroup. First, we extend a previous characterization by removing the square-free hypothesis on some fixed irreducible character degree. We then show the same arithmetic conditions follow from a faithful action of an abelian $π$-subgroup on the $π'$-part of the Fitting subgroup, where $π$ is the set of prime divisors of the aforementioned character degree.
