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On groups having a 𝑝-constant character
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-20 , DOI: 10.1090/proc/15256
Silvio Dolfi , Emanuele Pacifici , Lucía Sanus

Abstract:Let $ G$ be a finite group, and $ p$ a prime number; a character of $ G$ is called $ p$-constant if it takes a constant value on all the elements of $ G$ whose order is divisible by $ p$. This is a generalization of the very important concept of characters of $ p$-defect zero. In this paper, we characterize the finite $ p$-solvable groups having a faithful irreducible character that is $ p$-constant and not of $ p$-defect zero, and we will show that a non-$ p$-solvable group with this property is an almost-simple group.


中文翻译:

在具有𝑝恒定字符的组上

摘要:让$ G $一个有限群和$ p $一个质数;的字符$ G $被称为$ p $的常数,如果它需要对所有的元素的恒定值$ G $,其顺序是按整除$ p $。这是$ p $零缺陷字符非常重要的概念的概括。在本文中,我们表征了$ p $具有忠实不可约性的有限可解基团,这些特征是-$ p $恒定而不是-$ p $缺陷零,并且我们将证明$ p $具有此属性的不可解基团是几乎简单的基团。
更新日期:2020-10-20
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