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Approximation properties of nilpotent interlacings of groups

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The work is devoted to the study of properties of verbal products and interlacings of groups, in particular, the problem of approximability and finite approximability.

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References

  1. O. N. Golovin, “On associative operations on the set of groups,” Dokl. Akad. Nauk SSSR, 38, 1237–1260 (1947).

    MathSciNet  Google Scholar 

  2. O. N. Golovin, “Nilpotent products of groups,” Mat. Sb., 27, 427–545 (1950).

    MathSciNet  Google Scholar 

  3. O. N. Golovin, “Meta-Abelian products of groups,” Mat. Sb., 28, 431–444 (1951).

    MathSciNet  Google Scholar 

  4. O. N. Golovin, “On the question on the isomorphism of nilpotent expansions of a group,” Mat. Sb., 28, 334–352 (1951).

    Google Scholar 

  5. M. I. Kargapolov and E. I. Timoshenko, “On the question on finite approximability with respect to the conjugacy of meta-Abelian groups,” in: 4th All-Union Symp. on Group Theory, Novosibirsk (1973), pp. 86–88.

  6. Yu. A. Kolmakov, Approximation properties of some factorgroups, Ph.D. Thesis, MGU (1982).

  7. Yu. A. Kolmakov, “On the embedding into crossed products,” Sib. Mat. Zh., 26, No. 3, 63–72 (1985).

    MATH  MathSciNet  Google Scholar 

  8. Yu. V. Kuz'min, “Stable automorphisms of free polynilpotent groups,” Sib. Mat. Zh., 13, No. 4, 944–950 (1972).

    MathSciNet  Google Scholar 

  9. S. MacLane, Homology [Russian translation], Mir, Moscow (1966).

    MATH  Google Scholar 

  10. A. I. Mal'tsev, “On homomorphisms to finite groups,” Uch. Zap. Ivanovo Ped. Inst., 18, 49–60 (1958).

    Google Scholar 

  11. A. I. Mamuchishvili, “On the finite approximability of a nilpotent interlacing,” Soobshch. Akad. Nauk Georgian SSR, 76, No. 2, 301–303 (1971).

    Google Scholar 

  12. A. I. Mamuchishvili, “On the approximability of interlacings,” Nauch. Trudy GPI, 222, No. 1, 75–78 (1980).

    Google Scholar 

  13. A. I. Mamuchishvili, “On the approximability of a solvable product and interlacing of groups,” Nauch. Trudy GPI, 260, No. 3, 119–126 (1983).

    MathSciNet  Google Scholar 

  14. A. I. Mamuchishvili and A. Sh. Malkhasyan, On the Finite Approximability with Respect to the Conjugacy of Some Free Polynilpotent Groups [in Russian], deposited at VINITI, No. 1590-83.

  15. A. I. Mamuchishvili and A. Sh. Malkhasyan, “On a finite approximability with respect to the conjugacy of some free polynilpotent groups,” Sib. Mat. Zh., 25, No. 1, 209–210 (1984).

    Google Scholar 

  16. A. I. Mamuchishvili and V. M. Novik, “Notes on stable automorphisms of groups of one class,” Nauch. Trudy GPI, 237, No. 5, 76–81 (1981).

    Google Scholar 

  17. H. Neumann, Group Manifolds [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  18. G. A. Novak, “Stable homomorphisms with respect to free groups,” in: 14th All-Union Algebraic Conf., Thes. Repts., Pt. I, Novosibirsk (1977), p. 48.

  19. V. N. Remeslennikov and V. N. Sokolov, “Some properties on the Magnus embedding,” Algebra Logika, 9, No. 5, 566–578 (1970).

    MathSciNet  Google Scholar 

  20. V. N. Remeslennikov, “Finite approximability of groups with respect to the conjugacy,” Sib. Mat. Zh., 12, No. 5, 1085–1099 (1971).

    MathSciNet  Google Scholar 

  21. R. A. Sarkisyan, “Conjugacy in free polynilpotent groups,” Algebra Logika, 2, No. 6, 694–710 (1972).

    Google Scholar 

  22. R. A. Sarkisyan, “Stable automorphisms of some classes of groups,” Sib. Mat. Zh., 13, No. 5, 1031–1106 (1972).

    MathSciNet  Google Scholar 

  23. E. I. Timoshenko, “Conjugacy in free meta-Abelian groups,” Algebra Logika, 6, No. 2, 89–94 (1967).

    Google Scholar 

  24. M. Hall, Group Theory [Russian translation], Inostrannaya Literatura, Moscow (1962).

    Google Scholar 

  25. A. L. Shmel'kin, “Interlacings and manifolds of groups,” Izv. Akad. Nauk SSSR. Ser. Mat., 29, No. 1, 149–170 (1965).

    MATH  MathSciNet  Google Scholar 

  26. A. L. Shmel'kin, “Two remarks on free nilpotent groups,” Algebra Logika, 6, No. 2, 95–109 (1967).

    Google Scholar 

  27. A. L. Shmel'kin, “Finite approximability of a free product of groups,” in: Thes. Repts. XVI All-Union Algebraic Conf., Pt. I, Leningrad (1981), p. 179.

  28. A. L. Shmel'kin, “Approximation of a solvable product of groups,” in: Algebra, Collection of Papers Devoted to the 90th Birthday of O. Yu. Shmidt, MGU, Moscow (1982).

    Google Scholar 

  29. A. I. Eidelkind, “Verbal products of Magnus groups,” Mat. Sb., 85(127), No, 4, 504–526 (1971).

    MathSciNet  Google Scholar 

  30. N. Blackburn, “Conjugacy in nilpotent groups,” Proc. Amer. Math. Soc., 16, 143–148 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  31. D. E. Cohen, “Groups of cohomological dimension one,” Lect. Notes Math., 245, Springer-Verlag, Berlin-New York (1972).

    Google Scholar 

  32. K. W. Grünberg, “Residual properties of infinite soluble groups,” Proc. London Math. Soc. (3), 7, 29–62 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  33. C. K. Gupta and N. D. Gupta, “Generalized Magnus embeddings and some applications,” Math. Z., 160, No. 1, 75–87 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  34. P. Hall, “On the finiteness of certain soluble groups,” Proc. London Math. Soc. (3)., 9, 595–622 (1959).

    Article  MATH  MathSciNet  Google Scholar 

  35. L. Kaloujnine, “Sur les p-groupes de Sylow du groupe symetrique du degre p m,” C. R. Acad. Sci. Paris, 221, 222–224 (1945).

    MATH  MathSciNet  Google Scholar 

  36. F. W. Levi, “Notes on group theory.” J. Indian Math. Soc. (N.S.), 8, 1–9, 44–56, 78–91 (1994); 9, 37–42 (1995).

    Google Scholar 

  37. S. Moran, “Associative operations on groups. I,” Proc. London Math. Soc. (3), 6, 581–596 (1956).

    Article  MATH  MathSciNet  Google Scholar 

  38. J. R. Stallings, “On torsion-free groups with infinitely many ends,” Ann. Math. (2), 88, 312–334 (1968).

    Article  MathSciNet  Google Scholar 

  39. P. F. Stebe, “A residual property of certain groups,” Proc. Amer. Math. Soc., 26, 37–42 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  40. R. G. Swan, “Groups of cohomological dimension one,” J. Algebra, 12, 585–610 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  41. B. A. F. Wehrfritz, “Two examples of soluble groups that are not conjugacy separable,” J. London Math. Soc. (2), 7, 312–316 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  42. B. A. F. Wehrfritz, “Another example of a soluble group that is not conjugacy separable,” J. London Math. Soc. (2), 14, No. 2, 381–382 (1976).

    Article  MATH  MathSciNet  Google Scholar 

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  1. Georgian Technical University, Tbilisi, Georgia

    A. I. Mamuchishvili

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  1. A. I. Mamuchishvili
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 49, Algebra and Geometry, 2007.

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Mamuchishvili, A.I. Approximation properties of nilpotent interlacings of groups. J Math Sci 155, 709–747 (2008). https://doi.org/10.1007/s10958-008-9239-4

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