Generalizations of theorems of Magnus and Greendlinger

We obtain the generalizations of the well-known Magnus theorem on isomorphism of groups with one defining relation and Greendlinger's theorem on isomorphism of groups with condition $C'(\frac{1}{6})$ on the groups $C(6)$; $C(4)$ and $T(4)$, $C(3)$ and $T(6)$.