3 research outputs found
Construction of Steiner quasigroups containing a specified number of subquasigroups of a given order
AbstractIn this paper we give a construction for Steiner quasigroups containing a specified number of subquasigroups of a given order. In particular, we show that, if there is a Steiner quasigroup of order v, v Steiner quasigroups of order q, where q > v, pairwise intersecting in the same quasigroup of order p, then, if q > vp and q β p is not divisible by the order of any non-trivial, proper subquasigroup of V there is a Steiner quasigroup of order v(q β p) + p containing a copy of each of the v quasigroups of order q and no other subquasigroups of order q