The meaning of computer search in the study of some classes of IM-quasigroups

The IM-quasigroup C(q) for or is a GS-quasigroup. Some interesting geometric concepts can be introduced in a general GS-quasigroup and their nice geometric representations can be given in the mentioned GS-quasigroup which justifies the research of this quasigroup. The concept of a parallelogram can be defined by means of several equivalent formulae. Some of them can be obtained by means of a computer. We shall choose a suitable formula for the definition of a parallelogram which allows the characterization of GS-quasigroups by means of commutative groups.