Abstract
Let G be the Klein four-group and let be an arbitrary field of characteristic 2. A classification of indecomposable -modules is known. We calculate the relative cohomology groups for every indecomposable -module N, where χ is the set of proper subgroups in G. This extends work of Pamuk and Yalcin to cohomology with non-trivial coefficients. We also show that all cup products in strictly positive degree in are trivial.
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