Finite groups with mostly involuted cyclic subgroups

2025/08/01 by Vaibhav Chhajer, Chhajer, Vaibhav, Sharma, Palash
Mathematics · #Finite Group Theory Research #Limits and Structures in Graph Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2508.00681

Abstract

Let G be a finite group, define I(G)=\x∈ G : x²=1\, C(G)= set of the cyclic subgroups of G, i(G)=|I(G)| and c(G)=|C(G)|. In this article, we will classify finite groups with i(G)=c(G)-r for r=0,1, and 2. We also prove that the range of the function given by β(G)=(i(G))/(c(G)) is dense in [0,1].

Citations

• Finite groups with nearly half as many cyclic subgroups as elements
• Element orders in extraspecial groups
• A connection between the number of subgroups and the order of a finite group
• Finite Groups with a Prescribed Number of Cyclic Subgroups II
• Finite groups with many involutions

Related

• Finite groups with a certain number of cyclic subgroups II
• Finite groups with nearly half as many cyclic subgroups as elements
• Finite Groups with a Prescribed Number of Cyclic Subgroups
• Finite Groups with a Prescribed Number of Cyclic Subgroups II
• Element orders in extraspecial groups