Notation of a $G$-module in a group cohomology paper In the first page of the paper titled "The mod $p$-cohomology ring of $\operatorname{GL}_3(\mathbb{F}_p)$" (found here), there are two notational questions that pop up for me. I'll try to reproduce the relevant material here.
In Theorem 1, the notation $\mathbb{Z}_p[b]^+$ is used, where $p$ is a prime number, and for our purposes we can treat $b$ as an indeterminate. The description they give for this is that $\mathbb{Z}[-]^+$ is the "positive part" in $\mathbb{Z}_p[-]$, but I'm not sure what this means.
Also, the paper computes $H^*(\operatorname{GL}_3(\mathbb{F}_p),\mathbb{Z})_{(p)}$, which I take to be the abelian group
$$\bigoplus_{n\ge 0}H^n(\operatorname{GL}_3(\mathbb{F}_p),\mathbb{Z})_{(p)}$$
where $A_{(p)}$ is the $p$-primary part of an abelian group $A$ (the subgroup of elements with prime-power order). However, in Theorem 1, the authors use the notation $H^*(\operatorname{GL}_3(\mathbb{F}_p),\mathbb{Z}_{(p)})$, and I'm not entirely clear what to make of the object $\mathbb{Z}_{(p)}$. Is this the localization of $\mathbb{Z}$ at the prime ideal $(p)$, given the trivial $\operatorname{GL}_3(\mathbb{F}_p)$-module structure? If so, how can it be seen that
$$H^*(\operatorname{GL}_3(\mathbb{F}_p),\mathbb{Z}_{(p)})\cong H^*(\operatorname{GL}_3(\mathbb{F}_p),\mathbb{Z})_{(p)}$$
which is claimed later in the paper. Is there any relationship between this object and $H^*(\operatorname{GL}_3(\mathbb{F}_p),\mathbb{F}_{(p)})$? Thanks for any help and for clearing up my confusion.
 A: Yes, $\mathbb{Z}_{(p)}$ is the localization of $\mathbb{Z}$ at $(p)$, and presumably it is given the trivial module structure. Note that when $A$ is a finite abelian group then $A_{(p)}$, interpreted as the localization $A \otimes \mathbb{Z}_{(p)}$ of $A$ at $(p)$, is precisely the subgroup of elements of $p$-power order. 
The localization result follows from the observation that localization $(-) \mapsto (-) \otimes \mathbb{Z}_{(p)}$ is exact (equivalently, that $\mathbb{Z}_{(p)}$ is flat), and exact functors commute with taking (co)homology of (co)chain complexes, in this case the cochain complex computing group cohomology.
The relationship between $H^{\bullet}(-, \mathbb{Z}_{(p)})$ and $H^{\bullet}(-, \mathbb{F}_p)$ is that the short exact sequence
$$0 \to \mathbb{Z}_{(p)} \xrightarrow{p} \mathbb{Z}_{(p)} \to \mathbb{F}_p \to 0$$
induces a coefficient long exact sequence where the connecting homomorphisms are certain Bockstein homomorphisms. You can also get some information, slightly less directly, from the universal coefficient theorem for cohomology. 
