偶数字符度和伊藤-米克勒定理

IF 1.1 4区数学 Q1 MATHEMATICS

Communications in Mathematics and Statistics Pub Date : 2024-01-18 DOI:10.1007/s40304-023-00368-0

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引用次数: 0

摘要

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.

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Even Character Degrees and Ito–Michler Theorem

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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来源期刊

Communications in Mathematics and Statistics Mathematics-Statistics and Probability

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： Communications in Mathematics and Statistics is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences, University of Science and Technology of China (USTC). The journal will be committed to publish high level original peer reviewed research papers in various areas of mathematical sciences, including pure mathematics, applied mathematics, computational mathematics, and probability and statistics. Typically one volume is published each year, and each volume consists of four issues.