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(of corresponding dimensions). how can I prove this? I think my main stumbling block is my general ignorance of group cohomology.

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    To answer this, we need to know what is your definition of group cohomology.2012-01-05
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    I have only learned the definition contained in Dummit and Foote wherein it is defined to be $Ext_{\mathbb{Z}G}(\mathbb{Z},\mathbb{Z})$. Are there non-equivalent definitions?2012-01-05
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    All definitions are equivalent, but to prove something is equivalent to one of them you need to actually pick one of them!2012-01-05
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    By the way, it is usually best if the body of the question is self contained and, in particular, does not require the title to make sense (your titiel/question does not satisfy this condition): have you ever seen a book whose first sentence starts in the cover?2012-01-05
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    agreed! though I'm willing to work out the equivalence between your definition and mine if yours lends itself to a proof of the statement.2012-01-05

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