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Nov 19, 2015 at 23:32 comment added Oscar Randal-Williams You're right: I had overlooked that $k$ was a field.
Nov 19, 2015 at 19:48 vote accept Nick
Nov 19, 2015 at 19:47 comment added Nick Thank you for the answer. I think also we have $Ext^{n+1}_{kG}(N,k)\cong Ext^{n+1}_{kG}(k,N^*\otimes k)\cong Ext^{n+1}_{kG}(k,M)$ where $M$ as in the question.
Nov 19, 2015 at 0:08 history answered Oscar Randal-Williams CC BY-SA 3.0