Abstract
Let Γ be a finite group, and let Λ be any Artin algebra. It is shown that the group algebra ΛΓ is virtually Gorenstein if and only if ΛΓ' is virtually Gorenstein, for all elementary abelian subgroups Γ' of Γ. We also extend this result to cover the more general context. Precisely, assume that Γ is a group in Kropholler’s hierarchy HF, Γ' is a subgroup of Γ of finite index, and R is any ring with identity. It is proved that, in certain circumstances, that RΓ is virtually Gorenstein if and only if RΓ' is so.
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