Abstract
This chapter discusses the representation theory of finite groups. Every irreducible representation of a group G occurs as an irreducible constituent of the regular representation. The number of irreducible representations of G is the same as the number of principal indecomposable representations. The chapter presents a theorem regarding the number of inequivalent irreducible representations of the group G in an algebraically closed field F. The degree of a character is defined as the degree of the corresponding representation. In linear characters, the characters of degree one is called linear. As a representation of degree one is a number, it coincides with its character.
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