Projectively coresolved Gorenstein flat dimension of groups

In this paper, we introduce and study the projectively core solved Gorenstein flat dimension of a group G over a commutative ring R and we prove that this dimension enjoys all the properties of the cohomological and the Gorenstein cohomological dimension. We also provide good estimations for the Gorenstein global dimension of RG in terms of this dimension and the Gorenstein global dimension of R. Moreover, we study special cases of groups, such as LHF-groups, and show that for such a group every Gorenstein projective RG-module is Gorenstein flat when the global dimension of R is finite.(c) 2023 Elsevier Inc. All rights reserved.