有限简单线性群直幂的谱识别

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2023-04-26 DOI:10.1007/s10231-023-01336-9

Nanying Yang, Ilya Gorshkov, Alexey Staroletov, Andrey V. Vasil’ev

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引用次数: 1

摘要

有限群的谱是其元素阶的集合。我们对Kourovka Notebook中的问题20.58（a）给出了肯定的答案，证明了对于每一个正整数k，只要n是大于或等于\（56k^2）的2的幂，则简单线性群\（L_{n}（2）\）的第k次直接幂由其在有限群类中的谱唯一确定。

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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On recognition of direct powers of finite simple linear groups by spectrum

The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive integer k, the k-th direct power of the simple linear group \(L_{n}(2)\) is uniquely determined by its spectrum in the class of finite groups provided n is a power of 2 greater than or equal to \(56k^2\).

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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.