REPRESENTATION OF GROUPS BY HOMOMORPHISM

Abstract

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