Abstract: | In this paper we compute the abelian kernels of the monoids POIn and POPIn of all injective order preserving and respectively, orientation preserving, partial transformations on a chain with n elements. As an application, we show that the pseudovariety POPI generated by the monoids POPIn (n epsilon N) is not contained in the Mal'cev product of the pseudovariety POI generated by the monoids POIn (n epsilon N) with the pseudovariety Ab of all finite abelian groups. |