切尔马克-德尔加多度量作为正集上的映射

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-08-22 DOI:10.1007/s00013-024-02015-8

William Cocke, Ryan McCulloch

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引用次数: 0

摘要

有限群的 Chermak-Delgado 度量是一个函数，它赋予每个子群一个正整数。在本文中，我们给出了当一个群的 Chermak-Delgado 度量实际上是一个 posets 映射（即从子群网格到正整数的单调函数）时的必要条件和充分条件。我们还研究了当 Chermak-Delgado 度量局限于中心子时，它是递增的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The Chermak–Delgado measure as a map on posets

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The Chermak–Delgado measure as a map on posets

The Chermak–Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak–Delgado measure of a group is actually a map of posets, i.e., a monotone function from the subgroup lattice to the positive integers. We also investigate when the Chermak–Delgado measure, restricted to the centralizers, is increasing.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.