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

Anabanti, Chimere Stanley

doi:10.5802/crmath.130

Théorie des groupes

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

Anabanti, Chimere Stanley ¹

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

Comptes Rendus. Mathématique, Tome 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 :

Anabanti, Chimere Stanley ¹

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

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     journal = {Comptes Rendus. Math\'ematique},
     pages = {1135--1138},
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     url = {http://www.numdam.org/articles/10.5802/crmath.130/}
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Anabanti, Chimere Stanley. A question of Malinowska on sizes of finite nonabelian simple groups in relation to involution sizes. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1135-1138. doi : 10.5802/crmath.130. http://www.numdam.org/articles/10.5802/crmath.130/

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Cité par

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