ON GROUP ACTION AND COHOMOLOGY THEORY
DOI:
https://doi.org/10.24237/04.04.872Keywords:
Cohomology theory Group action Cohomology theory Bornological group groupAbstract
In this work, The concept of group action and cohomology group are considered with a lots of details. Group action is a concept in abstract algebra describe how group acts on a set. The motivation, goal, or need for studying the action is to study the effects of the groups on the sets such that divided the sets into orbits. The motivation and goal or need for considering the cohomology group it is to study the properties of such kind of group which can be constructed from special action, such that this action can be happened when there is action from a group Q on an abelian group M and construct Q -module . After constrict this kind of groups from that action and related these kind of groups by each other’s by group homorphisim. The techniques of group cohomology can be do it, when Q acts on a non-abelian Q-group, as a generalization of a module to non-abelian coefficients.
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