On CLT and non-CLT groups

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-04-15 DOI:10.1007/s10231-024-01450-2

Marius Tărnăuceanu

引用次数: 0

Abstract

In this note, we prove that for every integer \(d\ge 2\) which is not a prime power, there exists a finite solvable group G such that \(d\mid |G|\), \(\pi (G)=\pi (d)\) and G has no subgroup of order d. We also introduce the CLT-degree of a finite group and answer two questions about it.

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关于文化小组和非文化小组

在这篇笔记中，我们证明了对于每一个不是素幂的整数 \(d\ge 2\), 存在一个有限可解群 G，使得 \(d\mid |G|\), \(\pi (G)=\pi (d)\) 并且 G 没有阶为 d 的子群。我们还引入了有限群的 CLT 阶，并回答了关于它的两个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.