The cohomological index of free Z/p-actions is not additive with respect to join

Abstract Let p denote an odd prime. We show by example that the inequalities obtained in [6] for the behaviour of the cohomological index of a join of free Z / p -actions are sharp. Namely, for all odd integers k , l at least one of which is greater than one, we give examples of finite free Z / p -CW complexes of cohomological indices k and l whose join has index k + l + 1 and also examples where the join has index k + l − 1 .