Permutation dimensions of prime cyclic groups

Abstract

Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by replacing projective resolutions of ring modules with resolutions by p-permutation modules of modules over the group ring. We compute this invariant for cyclic groups of prime order.