# Modules & Representations

1. Aug 30, 2011

### OMM!

There is a Theorem that says FG-Modules are equivalent to group representations:

"(1) If $\rho$ is a representation of G over F and V = $F^{n}$, then V becomes an FG-Module if we define multiplication vg by: vg = v(g$\rho$), for all v in V, g in G.

(2) If V is an FG-Module and B a basis of V, then $\rho$: g $\mapsto$ $[g]_{B}$ is a representation of G over F, for all g in G"

I've been told and I have read that using FG-Modules is advantageous to using group representations, but what exactly is the advantage of this, other than getting results like Maschke's Theorem?!

Thanks for any help!