Mathematical Notes

, Volume 62, Issue 1, pp 44–49 | Cite as

A problem in the theory of formations of finite groups

  • A. F. Vasil'ev
Article
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Abstract

In 1968 Carter, Fisher, and Hawkes developed the method of extremal classes to study local formations and their critical groups in the class of finite solvable groups. In the present paper the problem of Shemetkov on the extension of this method to arbitrary finite groups is solved.

Key words

finite group local formation local screen extremal class solvable group closed formation quasi-hereditary screen 

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References

  1. 1.
    R. Carter, B. Fischer and T. Hawkes, “Extreme classes of finite soluble groups,”J. Algebra,9, No. 3, 285–313 (1968).MathSciNetGoogle Scholar
  2. 2.
    L. A. Shemetkov,Formations of Finite Groups [in Russian], Nauka, Moscow (1978).Google Scholar
  3. 3.
    K. Doerk and T. Hawkes,Finite Soluble Groups, Walter de Gruyter, Berlin-New York (1972).Google Scholar
  4. 4.
    V. N. Semenchuk, “Minimal non-\(\mathfrak{F}\)-groups,”Algebra i Logika [Algebra and Logic],18, No. 3, 348–382 (1979).MATHMathSciNetGoogle Scholar
  5. 5.
    B. Huppert and N. Blackburn,Finite Groups. III, Springer, Berlin-Heidelberg-New York (1982).Google Scholar
  6. 6.
    L. A. Shemetkov and A. N. Skiba,Formations of Algebraic Systems [in Russian], Nauka, Moscow (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. F. Vasil'ev
    • 1
  1. 1.F. Skorina Gomel State UniversityGomelBelarus

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