✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we show that if $1/8$ of elements of $G$ have order two, then $G$ is either a simple group isomorphic to $PSL_{2}(q)$, where $q\in\{7,8,9\}$ or $G\cong GL_{2}(4).\mathbb{Z}_2 In fact in this paper, we answer Problem 132 in [1].
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Let $G$ be a finite non-solvable group.
📊
Key Findings & Data:Let $G$ be a finite non-solvable group.
💡
Conclusion & Impact:In this paper, we show that if $1/8$ of elements of $G$ have order two, then $G$ is either a simple group isomorphic to $PSL_{2}(q)$, where $q\in\{7,8,9\}$ or $G\cong GL_{2}(4).\mathbb{Z}_2 In fact in this paper, we answer Problem 132 in [1].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Involution · classification of finite groups with
Abstract
Let $G$ be a finite non-solvable group. In this paper, we show that if $1/8$ of elements of $G$ have order two, then $G$ is either a simple group isomorphic to $PSL_{2}(q)$, where $q\in\{7,8,9\}$ or $G\cong GL_{2}(4).\mathbb{Z}_2 In fact in this paper, we answer Problem 132 in [1].
🔖
Cite This Article
AHANJİDEH, N., GHASEMABADI, M. F. (2022). On the structure of finite groups with the given numbers of involutions. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 15–22. https://ajindex.com/articles/651242