On non-closure degree for finite groups

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 [ ۰ , \frac{|G| - ۱}{|G|} ), with the result as ۰ if and only if H=G. Illustrations were done using both abelian and non-abelian groups relative to their normal subgroups.

کلیدواژه ها:

Finite group ، Normal Subgroup ، closure property of a group ، Quotient Group