Let be a finite group, and let be any Artin algebra. It is shown that the group algebra is virtually Gorenstein if and only if is virtually Gorenstein, for all elementary abelian subgroups of . We also extend this result to cover the more general context. Precisely, assume that is a group in Kropholler’s hierarchy , is a subgroup of of finite index, and is any ring with identity. It is proved that, in certain circumstances, that is virtually Gorenstein if and only if is so.
Abdolnaser Bahlekeh. Shokrollah Salarian. "Virtual Gorensteinness over group algebras." Kyoto J. Math. 55 (1) 129 - 141, April 2015. https://doi.org/10.1215/21562261-2848133