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Conditions under which a lattice is isomorphic to the lattice of subgroups of a group. (English. Russian original) Zbl 0438.20019
Algebra Logic 13(1974), 400-412 (1975); translation from Algebra Logika 13, 694-712 (1974).

20E15 Chains and lattices of subgroups, subnormal subgroups
20E05 Free nonabelian groups
20E07 Subgroup theorems; subgroup growth
06B25 Free lattices, projective lattices, word problems
06B15 Representation theory of lattices
Full Text: DOI EuDML
[1] M. Suzuki, Structure of a Group and Structure of a Lattice of Its Subgroups [Russian translation], IL, Moscow (1960). · Zbl 0091.02201
[2] M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], Nauka, Moscow (1972). · Zbl 0499.20001
[3] S. A. Anishchenko, ”Representation of modular lattices by lattices of subgroups,” Matem. Zap. Krasnoyarskogo Gos. Ped. In-ta, No. 1, 1-21 (1965).
[4] L. E. Sadovskii, ”Lattice isomorphisms of free groups and free products,” Matem. Sb.,14, No. 1-2, 155-173 (1944). · Zbl 0061.02502
[5] B. I. Plotkin, ”Problems of the theory of torsion-free groups,” Ukr. Matem. Zh.,8, No. 3, 325-329 (1956). · Zbl 0073.25403
[6] O. Ore, ”Structures and group theory, II,” Duke Math. J., No. 4, 247-269 (1938). · JFM 64.0055.01 · doi:10.1215/S0012-7094-38-00419-3
[7] P. G. Kontorovich and B. I. Plotkin, ”Lattices with additive basis,” Matem. Sb.,35, 187-192 (1954). · Zbl 0058.26105
[8] G. Baumslag, ”On generalized free products,” Math. Z.,78, 423-438 (1962). · Zbl 0104.24402 · doi:10.1007/BF01195185
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