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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'group cohomology'
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full generality by dublisk
Correction id: 2357
Filed on: 2003-08-08 22:21:45
Status: Accepted on 2003-08-12 09:41:01
Type: Addendum
Correction text:
| The second cohomology group is quite important too, as it classifyies group extensions. You should give a definition of the group cohomology as Ext_{ZG}^n( G , M ) , where ZG is the group ring over the integers, and M is an abelian group, and is a ZG-module by making G act trivially on M. The definition you give comes out of a specific resolution when calculating Ext, namely the Eilenberg-MacLane Bar Resolution. |
Comment from object owner alozano:
Thanks, I usually just work with the first two groups, but I realize I should have given a more general definition.
Alvaro
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The second cohomology group is quite important too, as it classifyies group extensions. You should give a definition of the group cohomology as Ext_{ZG}^n( G , M ) , where ZG is the group ring over the integers, and M is an abelian group, and is a ZG-module by making G act trivially on M. The definition you give comes out of a specific resolution when calculating Ext, namely the Eilenberg-MacLane Bar Resolution. |
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