In this thesis we present Latin squares, isotopy, quasigroups and loops. We prove that each quasigroup is isotopic to a group, therefore each isotopy class contains at least one loop. We focus on a relationship between quasigroups and Latin squares and show equivalence between Latin squares and Cayley tables of a quasigroup. Reason why this can not be generalised to groups is shown on a counterexample. Criteria which ensure Latin square is isotopic to a group, therefore based on a group, are presented. Functioning of those criteria is closely explained using examples and counterexamples. Quadrangle criterion and his variations are presented. Thomsen condition, which ensures a Latin square is based on an Abelian group, is also presented. Criteria based on permutations of rows and columns of a Cayley tabele is also introduced.
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