Hamiltonian degree of finite groups

Document Type : Research Paper

Authors

1 Department of Pure Mathematics and Center of Exellence in Analysis on Algebraic Structures, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi, United Arab Emirates

3 Department of Mathematics, Tafila Technical University, Tafila, Jordan

Abstract

This paper examines the probability of finite groups being Hamiltonian,a property defined by all subgroups being normal, and its implications for group structure analysis. To this end, we introduce the Hamiltonian degree, a novel extension of commutativity degrees in finite groups, and propose a comprehensive framework for its evaluation. Explicit formulas are derived for the Hamiltonian degree of dihedral groups, alongside general bounds applicable to broader group classes. Additionally, we explore its relationship to conjugacy class subgroups, shedding light on new structural connections within group theory.

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References

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International Journal of Group Theory
Volume 15, Issue 4 - Serial Number 4
December 2026
Pages 193-206

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History

  • Receive Date: 16 April 2025
  • Revise Date: 27 July 2025
  • Accept Date: 11 December 2025
  • Published Online: 27 December 2025

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