On non-closure degree for finite groups

Document Type : Research Paper

Authors

1 Department of Mathematics, Air Force Institute of Technology, Kaduna, Nigeria

2 Department of Mathematical Sciences, Universiti Teknologi Malaysia, Johor, Malaysia

3 Department of Mathematical Sciences, Bayero University, Kano, Nigeria

Abstract

The non-closure degree for a finite group $G$ has to do with obtaining a probability of selecting any pair of elements $x, y \in G$ such that $xy \notin H$, where $H$ is normal in $G$. It is shown in the paper that the probability lies in the interval $[ 0 , \frac{|G| - 1}{|G|}$ ), with the result as 0 if and only if $H=G$. Illustrations were done using both abelian and non-abelian groups relative to their normal subgroups.

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References

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Journal of Algebra and Related Topics
Volume 13, Issue 2
December 2025
Pages 109-117

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