Given a ring $k$, a finite group $G$ and a free $k$-module $M$ with a free action of $G$, why is $M$ a free module over the group ring $k[G]$? (how do I find a $k[G]$ basis for $M$?)
find a $k[G]$-module basis for a $k$ module with $G$ action
4
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group-cohomology