REPRESENTATION OF GROUPS BY HOMOMORPHISM
Representation theory
Character theory
Irreducible characters
Issacs [1] shows that if
* :GF 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 :GG 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.