MSC: 20D05, 20D60
DOI: 10.21538/0134-4889-2021-27-4-269-275
Full text
This paper is based on the results of the 2020 Ural Workshop on Group Theory and Combinatorics.
In this note we provide some counterexamples for the conjecture of Moretó on finite simple groups, which says that any finite simple group $G$ can be determined in terms of its order $|G|$ and the number of elements of order $p$, where $p$ the largest prime divisor of $|G|$. A new characterization of all sporadic simple groups and alternating groups is given. Some related conjectures are also discussed.
Keywords: Finite simple groups, quantitative characterization, the largest prime divisor
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Received November 14, 2020
Revised February 28, 2021
Accepted April 5, 2021
Funding Agency: The project was partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202001303) and sponsored by Natural Science Foundation of Chongqing, China (cstc2021jcyj-msxmX0511).
Jinbao Li, Department of Mathematics, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China, e-mail: leejinbao25@163.com
Wujie Shi (Corresponding author), Department of Mathematics, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China; School of Mathematics, Suzhou University, Suzhou 215006, P. R. China, shiwujie@outlook.com
Cite this article as: Jinbao Li, Wujie Shi. On Some Conjectures Related to Quantitative Characterizations of Finite Nonabelian Simple Groups, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 4, pp. 269–275.
Русский
Цзиньбао Ли, Вуджи Ши. О некоторых гипотезах, связанных с числовой характеризацией конечных неабелевых простых групп
В заметке приведены контрпримеры к гипотезе Морето, которая утверждает, что любая простая группа $G$ может быть охарактеризована своим порядком и количеством элементов порядка $p$, где $p$ - наибольший простой делитель порядка группы. Предложена новая характеризация всех спорадических простых групп и знакопеременных групп. Обсуждаются некоторые связанные гипотезы.
Ключевые слова: конечные простые группы, числовая характеризация, наибольший простой делитель
