On the lattice of all totally composition formations of finite groups

  • Aleksandr TsarevEmail author


It is shown that the lattice of all totally composition formations of finite groups is algebraic.


Finite group Formation of groups Satellite of formation Totally composition formation algebraic lattice of formations 

Mathematics Subject Classification

Primary 20F17 Secondary 20D10 



The author thanks the anonymous referee for the careful and thoughtful reading of this paper.


  1. 1.
    Doerk, K., Hawkes, T.: Finite Soluble Groups, De Gruyter Expositions in Mathematics, vol. 4. Walter de Gruyter, Berlin (1992)CrossRefzbMATHGoogle Scholar
  2. 2.
    Gaschütz, W.: Zur Theorie der endlichen auflösbaren Gruppen. Math. Z. 80(4), 300–305 (1963)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Guo, W.: Structure Theory for Canonical Classes of Finite Groups. Springer, Berlin (2015)CrossRefzbMATHGoogle Scholar
  4. 4.
    Safonov, V.G.: The property of being algebraic for the lattice of all \(\tau \)-closed totally saturated formations. Algebra Log. 45(5), 353–356 (2006)CrossRefGoogle Scholar
  5. 5.
    Safonov, V.G.: Characterization of the soluble one-generated totally saturated formations of finite groups. Sib. Math. J. 48(1), 150–155 (2007)CrossRefGoogle Scholar
  6. 6.
    Skiba, A.N.: Algebra of Formations. Belaruskaya Navuka, Minsk (1997). (in Russian) zbMATHGoogle Scholar
  7. 7.
    Shemetkov, L.A., Skiba, A.N.: Formations of algebraic systems. In: Sovremennaya Algebra. Nauka, Moscow (1989). (in Russian) Google Scholar
  8. 8.
    Skiba, A.N., Shemetkov, L.A.: Multiply \({\mathfrak{L}}\)-composition formations of finite groups. Ukrainian Math. J. 52(6), 898–913 (2000)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Tsarev, A.: Inductive lattices of totally composition formations. Rev. Colomb. Mat. 52(2), 161–169 (2018)CrossRefGoogle Scholar
  10. 10.
    Tsarev, A.A., Vorob’ev, N.N.: On a question of the theory of partially composition formations. Algebra Colloq. 21(3), 437–447 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Vorob’ev, N.N.: Algebra of Classes of Finite Groups. P.M. Masherov Vitebsk State University, Vitebsk (2012). (in Russian) Google Scholar
  12. 12.
    Vorob’ev, N.N., Tsarev, A.A.: On the modularity of a lattice of \(\tau \)-closed \(n\)-multiply \(\omega \)-composition formations. Ukrainian Math. J. 62(4), 453–463 (2010)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Vorob’ev, N.N.: On one question of the theory of local classes of finite groups. Probl. Algebra 14, 132–140 (1999)Google Scholar

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© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Department of MathematicsJeju National UniversityJejuSouth Korea
  2. 2.Department of Mathematics and ITP.M. Masherov Vitebsk State UniversityVitebskBelarus

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