有限非abel单群的大小与对合大小的关系的Malinowska问题

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2021-01-25 DOI:10.5802/CRMATH.130

C. Anabanti

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引用次数: 2

摘要

令In (G)表示有限群G中n阶元素的个数。Malinowska最近问了一个问题:“当存在两个非阿贝尔有限简单群S和G，且|G|和|S|的素数因子p1，···，pk满足2 = p1 <···< pk且对于所有i∈{1，···，k}，我们有|G| = |S|，那么最小的正整数k是什么?”本文解决了马林诺夫斯卡的问题。2020数学学科分类。20D60,20D06。资金。作者得到格拉茨工业大学和奥地利科学基金(FWF)的部分资助:P30934-N35, F05503, F05510。他还在尼日利亚恩苏卡大学工作。收稿2020年5月25日，改稿2020年10月6日，收稿2020年10月7日。

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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A question of Malinowska on sizes of finite nonabelian simple groups in relation to involution sizes

Let In (G) denote the number of elements of order n in a finite group G . Malinowska recently asked “what is the smallest positive integer k such that whenever there exist two nonabelian finite simple groups S and G with prime divisors p1, · · · , pk of |G| and |S| satisfying 2 = p1 < ·· · < pk and Ipi (G) = Ipi (S) for all i ∈ {1, · · · , k}, we have that |G| = |S|?”. This paper resolves Malinowska’s question. 2020 Mathematics Subject Classification. 20D60,20D06. Funding. The author is supported by both TU Graz and partial funding from the Austrian Science Fund (FWF): P30934-N35, F05503, F05510. He is also at the University of Nigeria, Nsukka. Manuscript received 25th May 2020, revised 6th October 2020, accepted 7th October 2020.

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.