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Group cohomology of dihedral group:D16

719 bytes added, 03:43, 16 January 2013
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group = dihedral group:D16|
connective = of}}
 
This article describes the homology and cohomology group of [[dihedral group:D16]], the dihedral group of order 16 and degree 8.
 
==Homology groups for trivial group action==
 
{{homology groups for trivial group action facts to check against}}
 
===Over the integers===
 
The homology groups with coefficients in the integers are given as follows:
 
<math>H_q(D_{16};\mathbb{Z}) = \left \lbrace \begin{array}{rl} \mathbb{Z}, & q = 0 \\ (\mathbb{Z}/2\mathbb{Z})^{(q + 3)/2}, & q \equiv 1 \pmod 4\\ (\mathbb{Z}/2\mathbb{Z})^{(q + 1)/2} \oplus \mathbb{Z}/8\mathbb{Z}, & q \equiv 3 \pmod 4 \\(\mathbb{Z}/2\mathbb{Z})^{q/2}, & q \mbox{ even }, q > 0 \\ \end{array}\right.</math>
 
The first few homology groups are as follows:
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