Let φ1, ... ,φd be commuting measure-preserving transformations, \( \phi ^l \equiv \phi _1^{l_1 } \phi _2^{l_2 } \cdot \cdot \cdot \phi _d^{l_d } ,\Phi = \left\{ {\phi ^l } \right\} \). The Kakutani-Rokhlin tower theorem is proved in a refined form for non-periodic groups Φ, and the Shannon-McMillan theorem is extended to ergodic groups. These results are used to extend recent isomorphism results to groups of transformations.