Comptes Rendus
Théorie des groupes
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.

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 ,,p k of |G| and |S| satisfying 2=p 1 <<p k and I p i (G)=I p i (S) for all i{1,,k}, we have that |G|=|S|?”. This paper resolves Malinowska’s question.

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DOI : 10.5802/crmath.130
Classification : 20D60, 20D06
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},
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     year = {2020},
     doi = {10.5802/crmath.130},
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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/

[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

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[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

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