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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
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Objective & Hypothesis:Let $G$ be a finite non-solvable group.
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Key Findings & Data:Let $G$ be a finite non-solvable group.
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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].
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Cite This Article
Ahanjideh, N., Ghasemabadi, M. F. (2015). On the structure of finite groups with the given numbers of involutions. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 1. https://ajindex.com/articles/1403320