Ukrainian Mathematical Journal

, Volume 51, Issue 12, pp 1824–1838 | Cite as

Structure of certain classes of groups with locally cyclic Abelian subgroups

  • M. F. Kuzennyi
  • S. V. Maznichenko


We investigate groups with locally cyclic Abelian subgroups. We give a constructive description of locally solvable groups of this type that contain a nonidentity periodic part; we also describe locally solvable groups all Abelian subgroups of which are cyclic.


Finite Group Cyclic Group Nilpotent Group Quotient Group Abelian Subgroup 
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  1. 1.
    L. Redei, “Das ‘Schiefe Produkt’ in Gruppentheorie mit Auwendungen,”Comment. Math. Helv.,20, 225–264 (1947).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Yu. A. Gol’fand, “On groups all subgroups of which are special,”Dokl. Akad. Nauk SSSR,60, No. 8, 1313–1315 (1948).zbMATHMathSciNetGoogle Scholar
  3. 3.
    S. S. Levishchenko and N. F. Kuzennyi,Finite Groups with Systems of Dispersible Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1997).Google Scholar
  4. 4.
    N. Blackburn, “Generalization of certain elementary theorems on p-groups,”Proc. London Math. Soc.,11, No. 41, 1–22 (1961).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    M. Hall, Jr.,The Theory of Groups, Macmillan, New York (1959).zbMATHGoogle Scholar
  6. 6.
    B. Huppert,Endliche Gruppen, Springer, Berlin (1967).zbMATHGoogle Scholar
  7. 7.
    S. N. Chernikov, “Groups with given properties of systems of infinite subgroups,”Ukr. Mat. Zh.,19, No. 6, 111–131 (1967).Google Scholar
  8. 8.
    A. Yu. Ol’shanskii, “Infinite groups with cyclic subgroups,”Dokl. Akad. Nauk SSSR,245, No. 4, 785–787 (1979).MathSciNetGoogle Scholar
  9. 9.
    A. Yu. Ol’shanskii, “Infinite groups with subgroups of prime orders,”Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 2, 309–321 (1980).MathSciNetGoogle Scholar
  10. 10.
    A. G. Kurosh,Theory of Groups [in Russian], Nauka, Moscow (1967).Google Scholar
  11. 11.
    N. F. Sesekin and A. I. Starostin, “On one class of periodic groups,”Usp. Mat. Nauk,9, No. 4, 225–228 (1954).zbMATHMathSciNetGoogle Scholar
  12. 12.
    S. N. Chernikov,Groups with Given Properties of a System of Subgroups [in Russian], Nauka, Moscow (1980).zbMATHGoogle Scholar
  13. 13.
    M. F. Kuzennyi, “Biprimary nondispersible groups the order of which is divided by at most the cube of a prime number,”Dop. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 973–977 (1974).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • M. F. Kuzennyi
    • 1
  • S. V. Maznichenko
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Kiev Pedagogical InstituteKiev

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