REPRESENTATION OF GROUPS BY HOMOMORPHISM

Issacs [1] shows that if (lambda): G →F^* is a homomorphism ( F^* is the multiplicative group of the field F) and G is a group, then one can define P (g)=((lambda) (g)) which is an F-representation of G of degree 1 affords (lambda) as character. [2,3,4] inspires us to do the following: given a homomorphism ƒ: G → G^* then we define a representation of G by the ƒ homomorphism from a given F-representation of P^*:G^*→ GL(n,F) of G^* as P= P^* º ƒ. We study this kind of representations and their associated characters.