关于有限群的公零

IF 0.6 4区 数学 Q3 MATHEMATICS
Mark L. Lewis, Lucia Morotti, Emanuele Pacifici, Lucia Sanus, Hung P. Tong-Viet
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引用次数: 0

摘要

设G是一个有限群,设\(\textrm{Irr}(G)\)表示G的不可约复字符的集合。如果存在\(\chi \in \textrm{Irr}(G)\)使得\(\chi (g)=0\)(即G是\(\chi \)的零),则元素\(g\in G\)称为G的消失元素,在这种情况下,G在G中的共轭类\(g^G\)称为消失共轭类。本文研究了关于消失元和消失共轭类的几个问题;特别地,我们考虑了确定有限群G的最小共轭类数的问题,使得每一个非线性\(\chi \in \textrm{Irr}(G)\)在其中一个上消失。我们还考虑了确定群的非线性不可约特征的最小数目,使其中两个具有公零的相关问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Common Zeros of Characters of Finite Groups

Let G be a finite group, and let \(\textrm{Irr}(G)\) denote the set of the irreducible complex characters of G. An element \(g\in G\) is called a vanishing element of G if there exists \(\chi \in \textrm{Irr}(G)\) such that \(\chi (g)=0\) (i.e., g is a zero of \(\chi \)) and, in this case, the conjugacy class \(g^G\) of g in G is called a vanishing conjugacy class. In this paper we consider several problems concerning vanishing elements and vanishing conjugacy classes; in particular, we consider the problem of determining the least number of conjugacy classes of a finite group G such that every non-linear \(\chi \in \textrm{Irr}(G)\) vanishes on one of them. We also consider the related problem of determining the minimum number of non-linear irreducible characters of a group such that two of them have a common zero.

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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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