Hamiltonian degree of finite groups

Erfanian, Ahmad; Al Tahan, Madeleine; Al-Kaseasbeh, Saba

doi:10.22108/ijgt.2025.144951.1956

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	Hamiltonian degree of finite groups
International Journal of Group Theory
دوره 15، شماره 4، اسفند 2026، صفحه 193-206 اصل مقاله (450.97 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2025.144951.1956
نویسندگان
Ahmad Erfanian¹؛ Madeleine Al Tahan²؛ Saba Al-Kaseasbeh^* ³
¹Department of Pure Mathematics and Center of Exellence in Analysis on Algebraic Structures, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
²Department of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi, United Arab Emirates
³Department of Mathematics, Tafila Technical University, Tafila, Jordan
چکیده
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.
کلیدواژه‌ها
Hamiltonian group؛ commutativity degree؛ Dihedral group

مراجع
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Hamiltonian degree of finite groups