Geodesic
Defining relations of a~free modular lattice of rank~$3$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 69-72.

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For a $3$-generated free modular lattice we obtain a system of $11$ defining relations and prove this set to be minimal.
Keywords: free modular lattices, defining relations. 
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A. G. Gein; M. P. Shushpanov. Defining relations of a~free modular lattice of rank~$3$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 69-72. http://geodesic.mathdoc.fr/item/IVM_2013_10_a6/

[1] Ore O., “Remarks on structures and group relations”, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, 85:32 (1940), 1–4 | MR | Zbl

[2] Ladzianska Z., “Modulyarnye podstruktury struktury”, Mat. časop., 24:1 (1974), 81–83 | MR

[3] Kolibiar M., “Distributive sublattices of a lattice”, Proc. Amer. Math. Soc., 34:2 (1972), 359–364 | DOI | MR | Zbl