A representation of finite group on special modules

Abstract

In this paper we introduced a new definition of a representation of finite group. Depending on that a module is a generalization of vector space, we defined a rep. of finite group G on a module . Which, in turn, prepares a generalization of the concept of representation on finite vector space. Many properties of this rep. are optained. We proved that for every rep.  of a finite group  on a module , each of the radical and   of  is a subrepresentation of , every subrepresentation of a completely reducible is also completely reducible, and every completely reducible representation on Artinian module is a direct sum of irreducible subreps of it.

We research in the extent of the effect of properties of the module on the reducibility and the complete reducibility of the rep on it, so we study it on special modules, and We proved many of its properties.