Authors' names: Stancu Radu institutions: univ. of Geneva A short abstract of the paper: Let $P$ be a $p\text{-}$group and $\Ff$ a full Frobenius system over $P$. The aim of this paper is to give necessary and sufficient conditions on a subgroup $Q$ of $P$ for the normalizer $\N \Ff Q$ to be $\Ff$ itself. This generalizes a result of Gilotti and Serena on finite groups. Current status: a preprint proposed to Jounal of Pure and Applied Algebra