Skip to main content
Log in

Direct Decompositions of Ω-Foliated Fitting Classes of Multioperator T-Groups

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

Studying direct decompositions for the Fitting classes of multioperator T-groups, we establish that the direct sum of n-multiply Ω-foliated Fitting classes of T-groups with right direction is also an n-multiply Ω-foliated Fitting class with right direction, and the converse holds for some right directions: free, canonical, etc.

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

References

  1. Kurosh A. G., Lectures on General Algebra [Russian], Nauka, Moscow (1973).

    MATH  Google Scholar 

  2. Neumann H., Varieties of Groups, Springer-Verlag, Berlin, Heidelberg, and New York (1967).

    Book  Google Scholar 

  3. Shemetkov L. A., Formations of Finite Groups [Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  4. Doerk K. and Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin and New York (1992).

    Book  Google Scholar 

  5. Skiba A. N., Algebra of Formations [Russian], Belarusskaya Nauka, Minsk (1997).

    MATH  Google Scholar 

  6. Skachkova Yu. A., “Boolean lattices of multiply Ω-foliated formations,” Discrete Math. Appl., vol. 12, no. 5, 477–482 (2002).

    Article  MathSciNet  Google Scholar 

  7. Kamozina O. V., “Boolean lattices of n-multiply Ω-bicanonical Fitting classes,” Discrete Math. Appl., vol. 12, no. 5, 483–489 (2002).

    Article  MathSciNet  Google Scholar 

  8. Vorobev N. N., Algebra of Classes of Finite Groups [Russian], Masherov VGU, Vitebsk (2012).

    MATH  Google Scholar 

  9. Demina E. N., “Boolean lattices of multiply Ω-foliated formations of multioperator T-groups,” in: Theory of Groups and Its Applications (Proceedings of the International VIII School-Conference Dedicated to the 75th Anniversary of V. A. Belonogov), KBGU, Nalchik, 2010, 86–93.

    Google Scholar 

  10. Vasilev A. F., Kamornikov S. F., and Semenchuk V. N., “On lattices of subgroups of finite groups,” in: Infinite Groups and Related Algebraic Systems [Russian], Inst. Mat. Akad. Nauk Ukrainy, Kiev, 1993, 27–54.

    Google Scholar 

  11. Ballester-Bolinches A., Doerk K., and Perez-Ramos M. D., “On the lattice of \(\mathfrak{F}\)-subnormal groups,” Algebra, vol. 148, no. 1, 42–52 (1992).

    Article  MathSciNet  Google Scholar 

  12. Vorobev N. N. and Skiba A. N., “On the boolean lattices of n times local Fitting classes,” Sib. Math. J., vol. 40, no. 3, 453–459 (1999).

    Article  Google Scholar 

  13. Higgins Ph. J., “Groups with multiple operators,” Matematika, vol. 3, no. 4, 55–106 (1959).

    Google Scholar 

  14. Vedernikov V. A. and Demina E. N., “Ω-Foliated formations of multioperator T-groups,” Sib. Math. J., vol. 51, no. 5, 789–804 (2010).

    Article  MathSciNet  Google Scholar 

  15. Vedernikov V. A. and Sorokina M. M., “Ω-Foliated formations and Fitting classes of finite groups,” Discrete Math. Appl., vol. 11, no. 5, 507–527 (2001).

    Article  MathSciNet  Google Scholar 

  16. Vedernikov V. A., “Maximal satellites of Ω-foliated formations and Fitting classes,” Proc. Inst. Math. Mech. (Supplementary issues), vol. 7, no. 2, S217–S233 (2001).

    MathSciNet  MATH  Google Scholar 

  17. Vedernikov V. A., “Subdirect products and formations of finite groups,” Algebra and Logic, vol. 29, no. 5, 348–361 (1990).

    Article  MathSciNet  Google Scholar 

  18. Shemetkov L. A. and Skiba A. N., Formations of Algebraic Systems [Russian], Nauka, Moscow (1989).

    MATH  Google Scholar 

  19. Bazhanova E. N. and Vedernikov V. A., “Ω-Foliated Fitting classes of T-groups,” Sib. Electron. Math. Rep., vol. 14, 629–639 (2017).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to E. N. Bazhanova or V. A. Vedernikov.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 283–296.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bazhanova, E.N., Vedernikov, V.A. Direct Decompositions of Ω-Foliated Fitting Classes of Multioperator T-Groups. Sib Math J 61, 222–232 (2020). https://doi.org/10.1134/S0037446620020044

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446620020044

Keywords

Navigation