Geodesic
On a~Functional Equation with a~Group Isotopy Property
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2005), pp. 65-71

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The set of all solutions of functional equation $F_1(F_2(z;x);F_3(y;z))=F_4(F_5(x;y);x)$ on quasigroup operations of an arbitrary fixed set are found. The result implies W. Dudek's theorem [1], which presents the operation in a quasigroup satisfying the identity $xy\cdot x=zx\cdot yz$. 
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     author = {Raisa Koval'},
     title = {On {a~Functional} {Equation} with {a~Group} {Isotopy} {Property}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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     number = {2},
     year = {2005},
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Raisa Koval'. On a~Functional Equation with a~Group Isotopy Property. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2005), pp. 65-71. http://geodesic.mathdoc.fr/item/BASM_2005_2_a3/