How does group cohomology relate to algebraic k-theory? In the wikapedia article on group cohomology (https://en.wikipedia.org/wiki/Group_cohomology#Algebraic_K-theory_and_homology_of_linear_groups) , there is a short section on how it relates to group cohomology, via the plus construction. 
First, is there an introductory source that I could read about this? (I haven't studied much group cohomology) 
Second, it is not even clear to me how it relates. Is there some equality between the two, such as $H^i(Gl(R)) = K_i(R)$?
Thank you!
 A: The Hurewicz map induces a canonical map
$K_n (R) \mapsto H_n(GL(n),\mathbb{Z})$,
which may both have a non-zero kernel and cokernel. In general that's about all you get. From this basic setup one can extract more though, e.g., statements of the type


*

*if all group homology groups happen to be finitely generated, so are all K-groups
(this is the strategy used to prove that K-groups of number fields and their rings of integers are finitely generated)

*many maps out of K-theory factor through this map, notably Chern characters; that includes for example the Borel regulator in the number field case,
so even if there is no connection as good as an isomorphism, it's quite useful.
Now, if you accept tensoring everything with $\mathbb{Q}$, things get much better. The full group homology is a Hopf algebra and there is an isomorphism
$K_n (R) \otimes \mathbb{Q} \mapsto \text{Prim} H_n(GL(n),\mathbb{Q})$,
where on the RHS Prim denotes the primitive elements. However, often the torsion in K-theory is quite interesting, (as is the torsion in group homology!), so this doesn't help if you care about torsion.
Finally, note that the computation of group homology of arithmetic groups is extraordinarily hard, say SL(Z) or even SL(Z[t]), even if you use computers, so we're comparing two things here which are both hard to attack.
Alexander Rahm is a good person to talk to if you care about group homology or rings of integers, done with computer assistance.
