Geodesic
A parallelogram configuration condition in nets
Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 5-17
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After describing a (general and special) coordinatization of $k$-nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in $k$-nets with small degree $k$.
After describing a (general and special) coordinatization of $k$-nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in $k$-nets with small degree $k$.
Classification : 05B25, 05B30, 20N05
Keywords: k-net; parallelogram “letter” condition; admissible relation and admissible algebra 
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Markvartová, Jitka. A parallelogram configuration condition in nets. Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 5-17. http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a2/

[1] Belousov, V. D.: Algebraic nets and quasigroups. Kishinev, 1971, in Russian.

[2] Havel, V.: General nets and their associated groupoids. Proc.Symp. “n-ary Structures” (1982), Skopje, 229-241. | MR | Zbl

[3] Havel, V.: Homomorphisms of nets of fixed degree with singular points on the same line. Czech. Math. Journ. 26 (1976), 43-54. | MR | Zbl