Let G be a finite group and k a field of characteristic p > 0. Balmer and Gallauer's recent result on finite p-permutation resolutions of kG-modules motivates the study of an intriguing new invariant; the p-permutation dimension. Following Walsh's success with cyclic groups of prime order, we compute the (global) p-permutation dimension of the Klein 4-group in characteristic p: = 2, along with the dimensions for each of its indecomposable modules.
Henry Harman (Tue,) studied this question.