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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
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 
be a finite group, and 
a prime number; a character of 
is called 
-constant if it takes a constant value on all the elements of 
whose order is divisible by 
. This is a generalization of the very important concept of characters of 
-defect zero. In this paper, we characterize the finite 
-solvable groups having a faithful irreducible character that is 
-constant and not of 
-defect zero, and we will show that a non-
-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：让一个有限群和一个质数；的字符被称为的常数，如果它需要对所有的元素的恒定值，其顺序是按整除。这是零缺陷字符非常重要的概念的概括。在本文中，我们表征了具有忠实不可约性的有限可解基团，这些特征是-恒定而不是-缺陷零，并且我们将证明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
be a finite group, and a prime number; a character of is called -constant if it takes a constant value on all the elements of whose order is divisible by . This is a generalization of the very important concept of characters of -defect zero. In this paper, we characterize the finite -solvable groups having a faithful irreducible character that is -constant and not of -defect zero, and we will show that a non--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
一个有限群和一个质数；的字符被称为的常数，如果它需要对所有的元素的恒定值，其顺序是按整除。这是零缺陷字符非常重要的概念的概括。在本文中，我们表征了具有忠实不可约性的有限可解基团，这些特征是-恒定而不是-缺陷零，并且我们将证明具有此属性的不可解基团是几乎简单的基团。
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