250043 VO Selected topics in algebraic: Cohomology of groups (2009W)

Group homology and cohomology has its origin in topology. With the rise of
the algebraic methods the homology and cohomology of several algebraic systems
was defined and explored.
We start the lecture by giving an elementary definition of group cohomology,
along with group extensions and factor systems. We give interpretations of
the n-th cohomology group for small n.
Then we study profinite groups and their cohomology, with coefficients
being discrete modules. These groups arise as Galois groups of
(possibly infinite) field extensions. Their cohomology is named Galois
cohomology, and is very important for number theory.
Finally we plan a short account on the functorial definition of cohomology.