Quantitative Relations between Commutativity, Surjectivity, and Homomorphism Degrees in Finite Groups

Authors : Mehmet Uc

Pages : 705-715

Doi:10.19113/sdufenbed.1818549

View : 49 | Download : 273

Publication Date : 2025-12-25

Article Type : Research Paper

Abstract :This article introduces two new probabilistic measures, the surjectivity degree and the homomorphism degree, for the purpose of structural analysis in finite groups. An analytical framework is developed that establishes a relationship be-tween these measures and the previously introduced commutativity degree. New lower and upper bounds for the commutativity degree, depending on the surjectiv-ity degree, are obtained; the homomorphism properties of functions between groups are quantitatively investigated. The relationships between the concepts are supported by theorems and examples, and SageMath code is provided for some examples. These findings contribute to a deeper probabilistic understanding of structural homomorphisms and provide new analytical tools for quantifying algebraic relationships within finite groups.
Keywords : Komütatiflik derecesi, Grup homomorfizması, Surjektiflik

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