The module structure of the n-th free metabelian Lie power Mn(ZG) of the regular module ZG

Let G be an arbitrary group, n a positive integer and Mn(ZG) the n-th free metabelian Lie power of the regular module ZG. In this thesis, the module structure of Mn(ZG) is studied. In the first chapter, some definitions and theorems necessary for the thesis are given. In the second chapter, free metabelian Lie algebras are introduced. In the third chapter, G-modules are considered and the definition of the regular module is given. In the fourth chapter, the direct decomposition of a permutation module and in the fifth chapter, the module structure of Mn(ZG) are explained. In the final chapter, some applications and examples of the results of the fifth chapter are given.