The central results of this article are two theorems onGŌandGprimitivity on relative level 1 of the Kac module⫫(⋀) for the Lie superal-gebraG=sl(m/n). These theorems are combined with Kac module homomorphisms in order to prove a conjecture by Hughes et al. [HKV] on the number of composition factors of the Kac module for 3- andr- fold atypical highest weights ofsl(3/3) andsl(rZ/r) respectively. Our theorems onGŌandGprimitivity are general in nature and therefore the results also include infinite-dimensional representations.