ON ORTHOGONAL SYSTEMS OF TERNARY QUASIGROUPS ADMITTING NONTRIVIAL PARATOPIES.

Abstract

In the present workwe describ eallorthogonal systems consisting of three ternary quasigroupop erations and of all (three) ternary selectors,admitting at least one nontrivial paratopy. In[11]we proved that there exist precisely 48 orthogonal systems of the considered form,admitting atleast one paratopy,which components are three quasigroupop erations,or two quasigroupop erations and a selector. Now we show that there exist precisely 105 such systems, admitting at least one nontrivial paratopy which comp onents are two selectors and a quasigroup op eration, or three selectors.