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Published online by Cambridge University Press: 17 December 2013
Let $\Gamma $ be a group and
${\Gamma }^{\prime } $ be a subgroup of
$\Gamma $ of finite index. Let
$M$ be a
$\Gamma $-module. It is shown that
$M$ is (strongly) Gorenstein flat if and only if it is (strongly) Gorenstein flat as a
${\Gamma }^{\prime } $-module. We also provide some criteria in which the classes of Gorenstein projective and strongly Gorenstein flat
$\Gamma $-modules are the same.