I'm trying to read (part of) "The Presentation Rank of a Direct Product of Finite Groups" / Cossey, Gruenberg, Kovacs (Journal Of Alegebra 28, 597-603 (1974)).
Here are some basic assertions I need help with:
(by context $p$ is a prime number and $G$ is a finite group)
For each $p$ dividing $|G|$, and each irreducible $\mathbb{F}_p G$-module $M$, let $E=\text{Hom}_G(M,M)$. Then: 1. $\text{Hom}_G(\mathbb{F}_p G,M) \cong E^{r_M}$, 2. $H^1(G,M) \cong E^{s_M}$, for certain non-negative integers $r_M$, $s_M$.
I am familiar with all terms except for "irreducible module". I know what a simple module is, and what an irreducible representation is. My guess is that irreducible module is just an old term for a simple module, but I'm not sure. So, I need help with this terminology issue and with the proof of both assertions.
Also note that this is my first encounter with group cohomlogy. I read the definition here: http://groupprops.subwiki.org/wiki/First_cohomology_group. I used to know a bit about cohomology in a topological context, but it's not fresh in my mind.