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Group cohomology of Klein four-group

519 bytes added, 00:44, 30 November 2011
Over an abelian group
These can be deduced from the homology groups with coefficients in the integers using the [[dual universal coefficients theorem for group cohomology]].
 
The first few groups are given below:
 
{| class="sortable" border="1"
! <math>p</math> !! <math>0</math> !! <math>1</math> !! <math>2</math> !! <math>3</math> !! <math>4</math> !! <math>5</math>
|-
| <math>H^p</math> || <math>M</math> || <math>(\operatorname{Ann}_M(2))^2</math> || <math>(\operatorname{Ann}_M(2)) \oplus (M/2M)^2</math> || <math>(\operatorname{Ann}_M(2))^2 \oplus (M/2M)</math> || <math>(\operatorname{Ann}_M(2))^2 \oplus (M/2M)^3</math> || <math>(\operatorname{Ann}_M(2))^4 \oplus (M/2M)^2</math>
|}
===Important case types for abelian groups===
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