Even Character Degrees and Ito–Michler Theorem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-18 DOI:10.1007/s40304-023-00368-0

引用次数: 0

Abstract

Let \(\textrm{Irr}_2(G)\) be the set of linear and even-degree irreducible characters of a finite group G. In this paper, we prove that G has a normal Sylow 2-subgroup if \(\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^m/\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^{m-1} < (1+2^{m-1})/(1+2^{m-2})\) for a positive integer m, which is the generalization of several recent results concerning the well-known Ito–Michler theorem.

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偶数字符度和伊藤-米克勒定理

Abstract 让 \(textrm{Irr}_2(G)\) 是有限群 G 的线性偶度不可还原字符集。在本文中，我们证明如果 \(\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^m/\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^{m-1} <；(1+2^{m-1})/(1+2^{m-2})\) for a positive integer m, which is the generalization of several recent results concerning the well-known Ito-Michler theorem.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.