关于单位元素的扭曲共轭类是子群的有限群

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-07-16 DOI:10.1007/s00013-024-02025-6

Chiara Nicotera

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引用次数: 0

摘要

我们考虑这样的群 G，即集合（[G,\varphi ]=\{g^{-1}g^{\varphi }|g\in G\}\）是 G 的每个自变形 \(\varphi \)的子群，并且我们证明存在这样一个群 G，它对于每个 \(n\in \mathbb N\) 都是有限的、n 类 n 的群。那么存在一个具有上述性质的无限非零能群，库赫罗和马祖洛夫的猜想 18.14（《库洛夫卡笔记》第 20 期，2022 年）是假的。

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On finite groups in which the twisted conjugacy classes of the unit element are subgroups

We consider groups G such that the set \([G,\varphi ]=\{g^{-1}g^{\varphi }|g\in G\}\) is a subgroup for every automorphism \(\varphi \) of G, and we prove that there exists such a group G that is finite and nilpotent of class n for every \(n\in \mathbb N\). Then there exists an infinite not nilpotent group with the above property and the Conjecture 18.14 of Khukhro and Mazurov (The Kourovka Notebook No. 20, 2022) is false.

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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.