Stable letter ($t$)

A stable letter is the new generator of an HNN extension which implements an isomorphism between two specified subgroups by conjugation. In the convention $ta{t}^{-1}=\varphi (a)$, it moves elements of the source subgroup $A$ to the target subgroup $B$; using $t^{-1}at=\varphi (a)$ reverses the naming convention.