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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.
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