Projective Extension Of Some Important Theorems Of Ordinary Representations Of Finite Groups

Ordinary representations of groups can be interpreted as modules over group alge-bras. This interpretation permits the use of module-theoretic language, in which many statements become more natural and their proof more simple. The same situation prevails for projective representations in which the role of the group algebra is played by the twisted group algebra.This paper is divided into four chapters:In the first chapter, we introduce the basic notions of projective representations, and present the background of this paper.In the second chapter,we provide some preliminary results that we need in this article.In the third chapter, we recall some concepts about twisted group algebra and definitions of projective representations.In the fourth chapter, we list some well-known results about ordinary representa-tions of finite groups and their extensions to projective representations and prove it.