The Permutation Dimension of the Klein 4-Group

Abstract Let G be a finite group and k a field of characteristic $$p > 0$$ 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 $$p := 2$$ p : = 2 , along with the dimensions for each of its indecomposable modules.