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

Chimere Stanley Anabanti

doi:10.5802/crmath.130

Théorie des groupes

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

Chimere Stanley Anabanti ¹

¹ Institut für Analysis und Zahlentheorie, Technische Universität Graz, Austria.

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1135-1138.

Résumé

Let $I_{n} (G)$ 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 $p_{1}, \dots, p_{k}$ of $| G |$ and $| S |$ satisfying $2 = p_{1} < \dots < p_{k}$ and $I_{p_{i}} (G) = I_{p_{i}} (S)$ for all $i \in {1, \dots, k}$ , we have that $| G | = | S |$ ?”. This paper resolves Malinowska’s question.

Reçu le : 2020-05-25
Révisé le : 2020-10-06
Accepté le : 2020-10-07
Publié le : 2021-01-25

DOI : 10.5802/crmath.130

Classification : 20D60, 20D06

Affiliations des auteurs :

Chimere Stanley Anabanti ¹

¹ Institut für Analysis und Zahlentheorie, Technische Universität Graz, Austria.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {A question of {Malinowska} on sizes of finite nonabelian simple groups in relation to involution sizes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1135--1138},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.130},
     language = {en},
}

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Chimere Stanley Anabanti. A question of Malinowska on sizes of finite nonabelian simple groups in relation to involution sizes. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1135-1138. doi : 10.5802/crmath.130. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.130/

Bibliographie
Cité par

[1] Chimere S. Anabanti A counterexample to Zarrin’s Conjecture on sizes of finite nonabelian simple groups in relation to involution sizes, Arch. Math., Volume 112 (2019) no. 3, pp. 225-226 | DOI | MR | Zbl

[2] Emil Artin The Orders of the Classical Simple Groups, Commun. Pure Appl. Math., Volume 8 (1955), pp. 455-472 | DOI | MR | Zbl

[3] Wieb Bosma; John Cannon; Catherine Playoust The Magma algebra system, 2019 (Version 2.24–5, http://magma.maths.usyd.edu.au/calc/)

[4] Daniel Gorenstein; Richard Lyons; Ronald Solomon The Classification of the Finite Simple Groups. Part I, Chapter A: Almost simple $K$ -groups, Mathematical Surveys and Monographs, 40, American Mathematical Society, 1998 | Zbl

[5] The GAP Group GAP – Groups, Algorithms, and Programming, 2020 (Version 4.11.0, https://www.gap-system.org)

[6] Marcel Herzog On the classification of finite simple groups by the number of involutions, Proc. Am. Math. Soc., Volume 77 (1979) no. 3, pp. 313-314 | DOI | MR | Zbl

[7] Wolfgang Kimmerle; Richard Lyons; Sandling Robert; David N. Teague Composition factors from the group ring and Artin’s theorem on orders of simple groups (3), Volume 60, London Mathematical Society, 1990 no. 1, pp. 89-122 | MR | Zbl

[8] Izabela Agata Malinowska Finite groups with few normalizers or involutions, Arch. Math., Volume 112 (2019) no. 5, pp. 459-465 | DOI | MR | Zbl

[9] Mohammad Zarrin A counterexample to Herzog’s Conjecture on the number of involutions, Arch. Math., Volume 111 (2018) no. 4, pp. 349-351 | DOI | MR | Zbl

Chimere Stanley Anabanti; Alireza Khalili Asboei Geometric mean Sylow numbers of nonsolvable groups, Quaestiones Mathematicae, Volume 48 (2025) no. 6, p. 903 | DOI:10.2989/16073606.2025.2459360
Alireza Khalili Asboei Groups with fewer than 15 involutions, Communications in Algebra, Volume 51 (2023) no. 10, pp. 4171-4175 | DOI:10.1080/00927872.2023.2198027 | Zbl:1521.20049
Chimere S. Anabanti; Jack Schmidt On some non-isomorphic simple groups with equalities on their number of elements orders, Communications in Algebra, Volume 51 (2023) no. 10, pp. 4176-4179 | DOI:10.1080/00927872.2023.2198035 | Zbl:1523.20032

Cité par 3 documents. Sources : Crossref, zbMATH

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