Some of the results obtained in the Yaroslavl branch algebraic school of~M.~D.~Grindlinger

V. G. Durnev ; O. V. Zetkina

Čebyševskij sbornik, Tome 15 (2014) no. 4, pp. 5-31.

Résumé

We review the main results obtained in the Yaroslavl branch of Martin Greendlinger's algebraic school from the middle 1970s up to the present. Bibliography: 93 titles.

Détail

Keywords: bound positive theories, equations in free groups and semigroups, verbal subgroups, algebraically closed groups.

Bibliographie

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[26] Durnev V. G., Zetkina O. V., “Equations with subsemigroup constraints to their solutions in free semigroups”, Chebyshevskii Sb., XI:3(35) (2010), 78–87 (Russian)

[27] Durnev V. G., “On equations with endomorphisms in free semigroups and groups”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1991, 30–35 (Russian)

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[30] Whitehead J. H. C., “On equivalent sets of elements in a free group”, Proc. London Math. Soc., 37 (1936), 782–800

[31] Durnev V. G., “NP-completeness of the problem of endomorphic reducibility for elements of a free semigroup of an countable rank”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 2003 (Russian)

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[37] Makanin G. S., “Equations in a free group”, Math. USSR-Izv., 21:3 (1983), 483–546 | DOI

[38] Makanin G. S., “Decidability of the universal and positive theories of a free group”, Math. USSR-Izv., 25:1 (1985), 75–88 | DOI

[39] Razborov A. A., “Systems of equations in a free group”, Izv. Akad. Nauk SSSR Ser. Mat., 48:4 (1984), 779–832 (Russian)

[40] Malkhasyan A. Sh., “On solvability in subgroups of equations in a free group”, Applied mathematics, 2, 1986, 42–47 (Russian)

[41] Durnev V. G., “On one generalization of the Problem 9.25 from the “Kourovka notebook”"”, Mathematical Notes, 47:2 (1990), 117–121 | DOI

[42] Durnev V. G., “Equations with constraints on the solution in free groups”, Mathematical Notes, 53:1 (1993), 26–29 | DOI

[43] Durnev V. G., “On equations with subgroup constraints on solutions in free groups”, Discrete Math. Appl., 5:6 (1995), 567–575 | DOI

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[45] Durnev V. G., Zetkina O. V., “On some equations with constraints to their solutions”, Chebyshevskii Sb., XI:3(35) (2010), 88–97 (Russian)

[46] Durnev V. G., “On the solvability problem for equations with a single coefficient”, Mathematical Notes, 59:6 (1996), 601–610 | DOI | DOI

[47] Durnev V. G., Zetkina O. V., “On the equations resolved with respect to variables in free groups with constraints to the solutions”, Chebyshevskii Sb., XIII:1(41) (2012), 63–80 (Russian)

[48] Durnev V. G., Zetkina O. V., “NP-complexity of the decidability problem for the equations with right-hand-side in a free group”, Chebyshevskii Sb., XIII:1(41) (2012), 46–53 (Russian)

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[51] Durnev V. G., “On one A. I. Mal'cev's question from the “Kourovka notebook””, Chebyshevskii Sb., XIII:1(41) (2012), 54–58 (Russian)

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[53] Durnev V. G., “On systems of equations on free nilpotent groups”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1981, 66–69 (Russian)

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[56] Roman'kov V. A., “Universal theory of nilpotent groups”, Mathematical notes of the Academy of Sciences of the USSR, 25:4 (1979), 253–258 | DOI

[57] Repin N. N., “Some simply defined groups without a decidability-testing algorithm”, Cybernetics, Calculation Complexity and Applied Mathematical Logics, M., 1988, 167–174 (Russian)

[58] Spielrein V. E., “On equations in the groups of $F/\gamma _{n}(R)$ type”, Algorithmic problems of groups and semigroups, Tula, 1990, 164–183 (Russian)

[59] Durnev V. G., “Undecidability of endomorphic reducibility problem for sets of elements of a free nilpotent group”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1988, 56–63 (Russian)

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[61] Durnev V. G., “The Mal'tsev–Nielsen equation in a free metabelian group of rank two”, Mathematical notes of the Academy of Sciences of the USSR, 46:6 (1989), 927–929 | DOI

[62] Maltsev A. I., “On the equation $zxyx^{-1}y^{-1}z^{-1}=aba^{-1}b^{-1}$ in a free group”, Algebra i Logika, 1:5 (1962), 45–50 (Russian)

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[65] Durnev V. G., “Undecidability of a positive $\exists$-theory with one constant for a free solvable group”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1992, 30–35 (Russian)

[66] Merzlyakov Yu. I., “Positive formulae on free groups”, Algebra i Logika, 5:4 (1966), 25–42 (Russian)

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[73] Durnev V. G., Kazarin L. S., “On unversal theories of some groups”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1994 (Russian)

[74] Durnev V. G., “Undecidability of some bounded theories of $SL(n, Z)$ and $GL(n, Z)$ ($n \geq 3$) groups”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl, 1994 (Russian)

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[77] Durnev V. G., “Semigroups with identities of some $F$-groups”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1998 (Russian)

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[79] Durnev V. G., “On width of the commutant of $B_3$ and $B_4$ braid groups”, XIX USSR algebraic conference, Book of abstracts (L'vov, 1987) (Russian)

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[86] Durnev V. G., Zetkina O. V., “On a positive theory of a free group in a signature extended by a length function”, Group Theory Homological Algebra, Yaroslavl' State University, Yaroslavl', 1991, 25–29 (Russian)

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