Steiner loops of affine type are associated to arbitrary Steiner triple systems. They behave to elementary abelian 3-groups as arbitrary Steiner Triple Systems behave to affine geometries over GF(3) GF ( 3 ) . We investigate algebraic and geometric properties of these loops often in connection to configurations. Steiner loops of affine type, as extensions of normal subloops by factor loops, are studied. We prove that the multiplication group of every Steiner loop of affine type with n elements is contained in the alternating group Aₙ A n and we give conditions for those loops having Aₙ A n as their multiplication groups (and hence for the loops being simple).
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Falcone et al. (2020) studied this question.