有限群的质因数与共轭类的个数

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-07-10 DOI:10.1017/s030500412300035x

THOMAS MICHAEL KELLER, ALEXANDER MORETÓ

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引用次数: 1

摘要

我们证明了存在一个普适常数D，使得如果p是有限群G的拟合子群的指标的素因子，则G的共轭类的个数至少为$Dp/\log_2p$。我们推测可以取D=1并且证明对于可解群，可以取D=1/3。

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Prime divisors and the number of conjugacy classes of finite groups

We prove that there exists a universal constant D such that if p is a prime divisor of the index of the Fitting subgroup of a finite group G, then the number of conjugacy classes of G is at least

$Dp/\log_2p$

. We conjecture that we can take

$D=1$

and prove that for solvable groups, we can take

$D=1/3$

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.