非弗罗贝纽斯群中的异变

arXiv - MATH - Group Theory Pub Date : 2024-09-05 DOI:arxiv-2409.03305

Daniele Garzoni

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引用次数: 0

摘要

我们证明，如果 $G$ 是一个阶数足够大的 $n$ 的传递置换群，那么要么 $G$ 是基元的和弗罗贝尼斯的，要么 $G$ 中derangements 的比例大于 1/(2n^{1/2})$。这很尖锐，概括了卡梅隆-科恩（Cameron-Cohen）和古拉尼克-万（Guralnick-Wan）的边界，并在很大程度上解决了古拉尼克-铁普（Guralnick-Tiep）的一个猜想。我们还给出了有限域上变项覆盖的应用。

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Derangements in non-Frobenius groups

We prove that if $G$ is a transitive permutation group of sufficiently large degree $n$, then either $G$ is primitive and Frobenius, or the proportion of derangements in $G$ is larger than $1/(2n^{1/2})$. This is sharp, generalizes substantially bounds of Cameron--Cohen and Guralnick--Wan, and settles a conjecture of Guralnick--Tiep in large degree. We also give an application to coverings of varieties over finite fields.

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arXiv - MATH - Group Theory

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