Given an elementary abelian p-group $G $ , it's well known that it can be seen as a vector space over $\mathbb{Z}_p $  .

But, does someone have an idea about possible sources where I can find proofs that use this fact? Examples: linear independence of elements in a group $G $ modulo $\phi(G) $ ($\phi(G)$ is the Frattini group of $G$ )  , etc...

Does someone have an idea?

Thanks  !

Given an elementary abelian $p$-group $G$, it's well known that it can be seen as a vector space over $\mathbb{Z}_p $.

But, does someone have an idea about possible sources where I can find proofs that use this fact? Examples: linear independence of elements in a group $G $ modulo $\phi(G) $ ($\phi(G)$ is the Frattini group of $G$ ), etc. ...

Does someone have an idea?

Thanks!