ON GORENSTEIN HOMOLOGICAL DIMENSIONS OF GROUPS

Abstract:

      Let k be a commutative ring with finite weak dimension and let G be a group. In this paper, we explore the criterion that a group G has finite Gorenstein homological dimension. It is shown that the finiteness of the Gorenstein homological dimension of G coincides with the finiteness of the Gorenstein weak dimension of the group ring kG. Furthermore, we give a Gorenstein analogy of the Serre's theorem. Some well-known results for the Gorenstein homological dimension of G over the integer ring are also extended.