Siberian Mathematical Journal

, Volume 53, Issue 6, pp 1105–1109 | Cite as

On local finiteness of some groups of period 12

  • D. V. LytkinaEmail author
  • V. D. Mazurov
  • A. S. Mamontov


The local finiteness is proven of all groups of period 12 in which the order of the product of every two involutions is at most 4.


periodic group locally finite group 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sanov I. N., “Solution of the Burnside problem for exponent four,” Leningrad. Gos. Univ. Uchen. Zap. Ser. Mat. Nauk, No. 55, 166–170 (1940).Google Scholar
  2. 2.
    Burnside W., “On an unsettled question in the theory of discontinuous groups,” Quart. J. Pure Appl. Math., 33, No. 2, 230–238 (1902).zbMATHGoogle Scholar
  3. 3.
    Hall M., “Solution of the Burnside problem for exponent six,” Illinois J. Math., 2, No. 4, 764–786 (1958).MathSciNetzbMATHGoogle Scholar
  4. 4.
    Neumann B. H., “Groups whose elements have bounded orders,” J. London Math. Soc., 12, 195–198 (1937).CrossRefGoogle Scholar
  5. 5.
    Lysenok I. G., “Proof of a theorem of M. Hall concerning the finiteness of the groups B(m, 6),” Math. Notes, 41, No. 3, 241–244 (1987).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Hall M., The Theory of Groups, Chelsea, New York (1976).zbMATHGoogle Scholar
  7. 7.
    Schmidt O. Yu., “Infinite soluble groups,” Mat. Sb., 17, No. 2, 145–162 (1945).Google Scholar
  8. 8.
    Lytkina D. V., “Structure of a group with elements of order at most 4,” Siberian Math. J., 48, No. 3, 283–287 (2007).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Coxeter H. S. M. and Moser W. O. J., Generators and Relations for Discrete Groups, Springer-Verlag, Berlin, Heidelberg, and New York (1980).Google Scholar
  10. 10.
    Schönert M., et al., Groups, Algorithms and Programming, Lehrstuhl D für Mathematik, RWTH, Aachen (1993).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • D. V. Lytkina
    • 1
    Email author
  • V. D. Mazurov
    • 2
  • A. S. Mamontov
    • 2
  1. 1.Siberian State University of Telecommunications and Information SciencesNovosibirsk State UniversityNovosibirskRussia
  2. 2.Sobolev Institute of Mathematics and Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations