Let $G$ be a group and let $x_1,\cdots,x_n\in G$ and let $A$ be the normal closure of $\{x_1,\cdots,x_n\}$; that is, the smallest (by inclusion) normal subgroup containing $\{x_1,\cdots,x_n\}$. Notice that even if $\{x_1,\cdots,x_n\}$ is a finite set, $A$ may not be a finitely generated subgroup.
I am wondering if there is any standard terminology for this case. Shall we call $x_1,\cdots,x_n$ "normal generators", or perhaps "conjugate generators" of $A$?