Symmetric quasigroups of odd order

AbstractQuasigroups of yet another type turn out to be related to Steiner Triple Systems, though the connection is rather loose and not as precise as in the various coordinatizing bijections described in [3]. However, families of pairs formed by abelian groups of odd order and quasigroups defined on the same set of elements have repeatedly been used in the literature to construct Large Sets [8] of Steiner Triple Systems. In Section 1, these quasigroups and their association with abelian groups are described, while Section 2 is devoted to applications to STSs