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Mathematical logic, algebra and number theory
Finite simple groups with two maximal subgroups of coprime orders
N. V. Maslovaab a Krasovskii Institute of Mathematics and Mechanics UB RAS, S. Kovalevskaya Str., 16, 620108, Yekaterinburs, Russia
b Ural Federal University, Turgeneva Str., 4, 620075, Yekaterinburs, Russia
Abstract:
In 1962, V. A. Belonogov proved that if a finite group $G$ contains two maximal subgroups of coprime orders, then either $G$ is one of known solvable groups or $G$ is simple. In this short note based on results by M. Liebeck and J. Saxl on odd order maximal subgroups in finite simple groups we determine possibilities for triples $(G,H,M)$, where $G$ is a finite nonabelian simple group, $H$ and $M$ are maximal subgroups of $G$ with $(|H|,|M|)=1$.
Keywords:
finite group, simple group, maximal subgroup, subgroups of coprime orders.
Received April 23, 2022, published December 12, 2023
Citation:
N. V. Maslova, “Finite simple groups with two maximal subgroups of coprime orders”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1150–1159
Linking options:
https://www.mathnet.ru/eng/semr1634 https://www.mathnet.ru/eng/semr/v20/i2/p1150
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Abstract page: | 51 | Full-text PDF : | 19 | References: | 13 |
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