2-coboundary for a group action
This article gives a basic definition in the following area: group cohomology
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This term is defined, and makes sense, in the context of a group action on an Abelian group. In particular, it thus makes sense for a linear representation of a group
Suppose we want to classify all groups which arise as the group extension with normal subgroup and quotient . One approach to describing such a group is to define a collection of coset representatives for in . This can be viewed as a map from to . Call the coset representative for . Define as the element of given by .
It turns out that if we pick two different collections of coset representatives and let and be the functions corresponding to them, then is a 2-coboundary.
Further information: second cohomology group