PROJECTIVE CHARACTER VALUES ON REAL AND RATIONAL ELEMENTS

IF 0.6 4区数学 Q3 MATHEMATICS Bulletin of the Australian Mathematical Society Pub Date : 2024-02-29 DOI:10.1017/s0004972724000030

R. J. HIGGS

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引用次数: 0

Abstract

Let

$\alpha $

be a complex-valued

$2$

-cocycle of a finite group G with

$\alpha $

chosen so that the

$\alpha $

-characters of G are class functions and analogues of the orthogonality relations for ordinary characters are valid. Then the real or rational elements of G that are also

$\alpha $

-regular are characterised by the values that the irreducible

$\alpha $

-characters of G take on those respective elements. These new results generalise two known facts concerning such elements and irreducible ordinary characters of

$G;$

however, the initial choice of

$\alpha $

from its cohomology class is not unique in general and it is shown the results can vary for a different choice.

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实元素和有理元素上的射影特征值

让 $\alpha $ 是有限群 G 的复值 $2$ -环，其中 $\alpha $ 的选择使得 G 的 $\alpha $ - 字符是类函数，并且普通字符的正交关系的类似物有效。那么，G 的实元素或有理元素也是 $\alpha $ 规则的，它们的特征就是 G 的不可还原 $\alpha $ 字符在这些元素上的取值。这些新结果概括了关于这类元素和 $G 的不可还原普通字符的两个已知事实；$ 然而，从其同调类中初始选择 $\alpha $ 一般来说并不是唯一的，而且结果表明不同的选择会有不同的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society

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