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If $A$ is a lattice (i.e. a fin. gen. free $\mathbb{Z}$-module), and $G$ is some group which acts on $A$, will $A$ be a projective $\mathbb{Z}[G]$-module?

Thanks

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Clearly not, as the action can be trivial!

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    Notice that there are many other actions which will give non-projective modules, also.2012-12-20