Abstrakt
Let Q be a quasigroup. For let be the principal isotope.
Put and assume that. Then , and for every there is , where.
If G is a group and is an orthomorphism, then for every. A detailed case study of is made for the situation when , and both and are "natural" near-orthomorphisms.
Asymptotically, if G is an abelian group of order n. Computational results: and , where.
There are also determined minimum values for a(G(alpha,beta)), G a group of order <= 8.