Algebra and Logic

, Volume 8, Issue 1, pp 72–76 | Cite as

On the lower central series of a free product of groups

  • A. L. Shmel'kin


Mathematical Logic Free Product Central Series Lower Central Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann.,111, 259–280 (1935).Google Scholar
  2. 2.
    W. Magnus, Über Beziehungen zwischen höheren Kommutatoren, J. Reine Angew. Math.,177, 105–115 (1937).Google Scholar
  3. 3.
    E. Witt, Treue Darstellung Liescher Ringe, J. Reine Angew. Math.,177, 152–160 (1937).Google Scholar
  4. 4.
    G. Baumslag, ,“Groups with the same lower central sequence as relatively free groups. I. The Groups,” Trans. Amer. Math. Soc.,129, No. 2, 308–321 (1967).Google Scholar
  5. 5.
    K. W. Gruenberg, ,“Residual properties of infinite soluble groups,” Proc. London Math. Soc.,7, No. 25, 29–62 (1957).Google Scholar
  6. 6.
    A. L. Shmel'kin, ,“Free polynilpotent groups,” Izv. Akad. Nauk SSSR, Ser. Matem.,28, No. 1, 91–122 (1964).Google Scholar
  7. 7.
    É. B. Kikodze, ,“On free groups of certain varieties,” Algebra i Logika,5, No. 4, 15–23 (1966).Google Scholar
  8. 8.
    Yu. M. Gorchakov, ,“On central series of free groups of varieties,” Algebra i Logika,6, No. 3, 13–24 (1967).Google Scholar
  9. 9.
    Yu. M. Gorchakov, ,“Multinilpotent groups,” Algebra i Logika,6, No. 3, 25–30 (1967).Google Scholar
  10. 10.
    A. L. Shmel'kin, ,“Nilpotent products and torsion-free nilpotent groups,” Sibirsk. Matem. Zh.,3, No. 4, 625–640 (1962).Google Scholar
  11. 11.
    R. Ree, ,“Commutator groups of free products of torsion-free Abelian groups,” Ann. Math., (2), 66, 380–394 (1957).Google Scholar
  12. 12.
    A. I. Shirshov, ,“On one hypothesis in the theory of Lie algebras,” Sibirsk. Matem. Zh.,3, No. 2, 297–301 (1962).Google Scholar
  13. 13.
    K. K. Andreev, ,“Nilpotent groups and Lie algebras,” Algebra i Logika,7, No. 4, 4–14 (1968).Google Scholar
  14. 14.
    A. I. Shirshov, ,“On free Lie rings,” Matem. Sb.,45, No. 2, 113–122 (1958).Google Scholar
  15. 15.
    A. I. Mal'tsev, ,“Generalized nilpotent algebras and their associated groups,” Matem. Sb.,25, 347–366 (1949).Google Scholar
  16. 16.
    M. Lasard, ,“Sur les groupes nilpotentes des anneaux de Lie,” Ann. Sci. Ecole Norm. Sup., (3), 77, 101–190 (1954).Google Scholar

Copyright information

© Consultants Bureau 1970

Authors and Affiliations

  • A. L. Shmel'kin

There are no affiliations available

Personalised recommendations