关于群类群有亏集的概率的注释

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2025-09-22 DOI:10.1007/s00012-025-00906-7

Carles Cardó

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引用次数: 0

摘要

如果\(|X \cdot X|\le |X|\)，则群类群的子集X是亏的。众所周知，一个随机群类群存在一个含有\(t\ge 3\)的亏缺t元素集的概率为零。然而，我们相信对于2元素集合，概率不为零。我们证明它确实不是空的，并计算出确切的值。我们探讨了关于亏集及其似然的一些推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A note on the probability of a groupoid having deficient sets

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A note on the probability of a groupoid having deficient sets

A subset X of a groupoid is said to be deficient if \(|X \cdot X|\le |X|\). It is well-known that the probability that a random groupoid has a deficient t-element set with \(t\ge 3\) is zero. However, it is believed that the probability is not zero for 2-element sets. We prove that it is indeed not null and calculate the exact value. We explore some generalisations on deficient sets and their likelihoods.

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来源期刊

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.