Skip to main content
Log in

Finite groups generated by two nilpotent subgroups

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

Some criteria for the solvability of ABA groups with nilpotent subgroups A and B of special form are proved. An ABA group is a group of the form G = ABA, where A and B are subgroups of the group G.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. M. M. Guterman, “On ABA-groups of finite order,” Trans. Amer. Math. Soc.,139, No. 104, 109–145 (1969).

    Google Scholar 

  2. D. Gorenstein, “On finite groups of the form ABA,” Canad. J. Math.,14, No. 2, 195–236 (1962).

    Google Scholar 

  3. D. Gorenstein and J. N. Herstein, “A class of solvable groups,” Can. J. Math.,11, 311–320 (1959).

    Google Scholar 

  4. M. Hall, Theory of Groups, Macmillan (1961).

  5. W. Feit and J. G. Thompson, “Solvability of groups of odd order,” Pac. J. Math.,13, 775–1029 (1963).

    Google Scholar 

  6. G. Glaubermann, “Central elements in core-free groups,” J. Algebra,4, 403–420 (1966).

    Google Scholar 

  7. D. Gorenstein, “Finite groups in which Sylow 2-subgroups are abelian and centralizers of involutions are solvable,” Can. J. Math.,17, 860–906 (1965).

    Google Scholar 

  8. B. Huppert, Endliche Gruppen, I, Berlin-Heidelberg-New York (1967).

  9. A. V. Romanovskii, “Groups with Hall normal divisors,” in: Finite Groups [in Russian], Minsk (1966), pp. 98–115.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 11, No. 3, pp. 293–298, March, 1972.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Doktorov, I.P. Finite groups generated by two nilpotent subgroups. Mathematical Notes of the Academy of Sciences of the USSR 11, 183–185 (1972). https://doi.org/10.1007/BF01098522

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01098522

Keywords

Navigation