RELATIVE GROUP COHOMOLOGY AND THE ORBIT CATEGORY

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2014-07-03
Pamuk, Semra
YALÇIN, ERGÜN
Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups HG with rkHrkG-1. We answer this question negatively by calculating the relative group cohomology FH*(G, ?(2)) where G = Z/2xZ/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology FH*(G, M) can be calculated using the ext-groups over the orbit category of G restricted to the family F. In second part of the paper, we discuss the construction of a spectral sequence that converges to the cohomology of a group G and whose horizontal line at E-2 page is isomorphic to the relative group cohomology of G.

Citation Formats
S. Pamuk and E. YALÇIN, “RELATIVE GROUP COHOMOLOGY AND THE ORBIT CATEGORY,” COMMUNICATIONS IN ALGEBRA, vol. 42, no. 7, pp. 3220–3243, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48409.