The H – normalizer property

الملخص EN

We divide this research into two parts: In the first one, we will give a new formula of the normalizer property which we called the H–normalizer property.

The second part talks about the uf–normalizer property, as a special case of the H-normalizer property, which is considered by Yeanling Li in [3].

Our most important result is theorem 2.7 which gives a necessary and sufficient condition for which the finite group G satisfies the uf-normalizer property.