Abelian Kernels of Some Monoids of Injective Partial Transformations and an Application
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In this paper we compute the abelian kernels of the monoids POI n and POPI n 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 POPI n (n epsilon N) is not contained in the Mal'cev product of the pseudovariety POI generated by the monoids POI n (n epsilon N) with the pseudovariety Ab of all finite abelian groups.
KeywordsAbelian Group Order Preserve Orientation Preserve Partial Transformation Finite Abelian Group
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