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Quasi-identities in a free group. (English. Russian original) Zbl 0364.20035

Algebra Logic 15(1976), 25-33 (1977); translation from Algebra Logika 15, 39-52 (1976).

MSC:

20E05 Free nonabelian groups
20E10 Quasivarieties and varieties of groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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References:

[1] ”Competition problems for the 10th All-Union Algebra Colloquium,” Algebra i Logika, 8, No. 1, 3–4 (1969).
[2] Kourowskaya Notebook (Unsolved Problems in Group Theory), 4th edition, Novosibirsk (1973).
[3] W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, Interscience, New York (1966).
[4] A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).
[5] A. I. Budkin and V. A. Gorbunov, ”On the theory of quasivarieties of algebraic systems”, Algebra i Logika,14, No. 2, 123–142 (1975). · Zbl 0317.08003
[6] G. Baumslag, ”On generalized free products”, Math. Z.,78, No. 5, 423–438 (1962). · Zbl 0104.24402 · doi:10.1007/BF01195185
[7] B. B. Newman, ”The soluble subgroups of a one-relator group with torsion”, J. Austral. Math. Soc.,16, No. 3, 278–285 (1973). · Zbl 0274.20042 · doi:10.1017/S1446788700015044
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