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Configurations of rank eight in 3-nets. (Russian) Zbl 0646.20060
The author presents all the 21 configurations with just 8 vertices and with just three edges through every vertex, which can be embedded into 3- nets. Moreover, he deduces corresponding loop identities in coordinatizing loops. The start point is the counting of all (?) the 156 8-vertices-configurations without embedding into 3-nets [in: Mat. Issled. 51, 93-104 (1979; Zbl 0451.51002)]; but this list cannot be controlled without more difficulties. The reviewer remarks that the direct listing of all 3-net-configurations having a prescribed number of vertices with the help of computer is simpler and clearer. This will appear in a forthcoming paper of the reviewer and J. Klouda.
Reviewer: V.Havel
MSC:
20N05 Loops, quasigroups
51A20 Configuration theorems in linear incidence geometry
Citations:
Zbl 0451.51002
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