engleski

Pentagonal quasigroups

In this paper the concept of pentagonal quasigroup is introduced as {; ; ; IM}; ; ; -quasigroup satisfying the additional property of pentagonality. Some basic identities which are valid in a general pentagonal quasigroup are proved. Four different models for pentagonal quasigroups and their mutual relations are studied. Geometric interpretations of some properties and identities are given in the model $C(q)$, where $q$ is a solution of the equation $q^4-3q^3+4q^2-2q+1=0$.

IM-quasigroup ; regular pentagon

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