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This paper classifies all groupoids that have the property that every map from the groupoid to itself is either an endomorphism or a multiplication map.
Let G be a group with a dihedral subgroup H of order 2p
, where p is an odd prime. We show that if there exist H-connected transversals in G, then G is a solvable group. We apply this result to the loop theory and show that if the inner mapping group of a finite loop Q is dihedral of order 2p...
Let S be a semigroup. In this paper, projective S-acts and exact sequences in S-Act are studied. It is shown that, for a unitary S-act P, the functor Hom(P, –) is exact if and only if P ≅ Se for some idempotent e ɛ S.
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