UDC 512.542
MSC: 20D06, 20E28, 20E45
DOI: 10.21538/0134-4889-2026-32-1-197-205
This research was carried out within the State Contract of the Sobolev Institute of Mathematics (FWNF-2026-0017).
Given an automorphism $x$ of order bigger than $2$ of a sporadic simple group $S$, we show that there are at most $3$ conjugates of $x$ required to generate a subgroup of order divisible by a fixed prime divisor $r$ of $|S|$. The only exception is the case where $S=Suz$, $x$ is in class $3A$, $r=11$, and then the required number of generators is $4$.
Keywords: sporadic group, conjugacy, generators
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Funding Agency: This research was carried out within the State Contract of the Sobolev Institute of Mathematics (FWNF-2026-0017).
Danila O. Revin, Dr. Phys.-Math. Sci., Prof., Sobolev Institute of Mathematics of the Siberia Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia; Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia, e-mail: revin@math.nsc.ru. ORCID: 0000-0002-8601-0706
Andrei V. Zavarnitsine, Dr. Phys.-Math. Sci., Prof., Sobolev Institute of Mathematics of the Siberia Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia. e-mail: zav@math.nsc.ru. ORCID: 0000-0003-1983-3304
Cite this article as: Danila O. Revin, Andrei V. Zavarnitsine. Refined conjugate generation in sporadic groups. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 1, pp. 197–205.
Русский
Д.О. Ревин, А.В. Заварницин. Уточнение порождения сопряженными элементами в спорадических группах
Для автоморфизма $x$ порядка больше $2$ спорадической простой группы $S$ показано, что существует не более трех сопряженных с $x$ элементов, порождающих подгруппу, порядок которой делится на фиксированный простой делитель $r$ порядка группы $S$. Единственным исключением является случай, когда $S=Suz$, $x$ лежит в классе $3A$, $r=11$, и тогда требуемое число порождающих равно $4$.
Ключевые слова: спорадические группы, сопряженность, порождающие элементы
