An explicit basis for the admissible inference rules of the modal logics extending $S4.1$ and $Grz$

We study bases for the admissible inference rules in a broad class of modal logics. We construct an explicit basis for all admissible rules in the logics $S4.1$, $Grz$, and their extensions whose number is at least countable. The resulting basis consists of an infinite sequence of rules in a concise and simple form. In the case of a logic of finite width a basis for all admissible rules consists of a finite sequence of rules.