Glasnik Matematicki, Vol. 42, No.2 (2007), 319-343.

ALTERNATE PROOFS OF TWO CHARACTERIZATION THEOREMS OF MILLER AND JANKO ON 2-GROUPS, AND SOME RELATED RESULTS

Yakov Berkovich

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
e-mail: berkov@math.haifa.ac.il


Abstract.   We study the p-groups all of whose nonabelian maximal subgroups are decomposable in direct or central product of two groups with specific structures.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Minimal nonabelian p-groups, p-groups of maximal class, minimal non Dedekindian 2-groups, direct product, central product.


Full text (PDF) (free access)

DOI: 10.3336/gm.42.2.07


References:

  1. Y. Berkovich, On subgroups of finite p-groups, J. Algebra 224 (2000), 198-240.
    MathSciNet     CrossRef

  2. Y. Berkovich, On abelian subgroups of finite p-groups, J. Algebra 199 (1998), 262-280.
    MathSciNet

  3. Y. Berkovich, On subgroups and epimorphic images of finite p-groups, J. Algebra 248 (2002), 472-553.
    MathSciNet     CrossRef

  4. Y. Berkovich, Alternate proofs of some basic theorems of finite group theory, Glas. Mat. Ser. III 40 (2005), 207-233.
    MathSciNet     CrossRef

  5. Y. Berkovich, Groups of Prime Power Order, Part I, in preparation.

  6. Y. Berkovich and Z. Janko, Groups of Prime Power Order, Part II, in preparation.

  7. Y. Berkovich and Z. Janko, Structure of finite p-groups with given subgroups, Cont. Math. 402 (2006), 13-93.
    MathSciNet

  8. Y. Berkovich and Z. Janko, On subgroups of finite p-groups, Israel J. Math., to appear.

  9. Ya. G. Berkovich and E. M. Zhmud', Characters of Finite Groups, Part 1, AMS, Providence, RI, 1998.
    MathSciNet

  10. N. Blackburn, On a special class of p-groups, Acta Math. 100 (1958), 45-92.
    MathSciNet     CrossRef

  11. I. M. Isaacs, Character Theory of Finite Groups, Acad. Press, NY, 1976.
    MathSciNet

  12. Z. Janko, personal communication.

  13. Z. Janko, On finite nonabelian 2-groups all of whose minimal nonabelian subgroups are of exponent 4, J. Algebra 315 (2007), 801-808.
    MathSciNet     CrossRef

  14. Z. Janko, Finite 2-groups all of whose nonabelian subgroups are generated by involutions, Math. Z. 252 (2006), 419-420.
    MathSciNet     CrossRef

  15. G. A. Miller, The groups in which every subgroup is either abelian or hamiltonian, Trans. Amer. Math. Soc. (1907), 25-29.
    MathSciNet     CrossRef

  16. G. A. Miller, The groups in which every subgroup is either abelian or dihedral, Amer. Math. J. 29 (1907), 289-294.
    MathSciNet     CrossRef

  17. G. A. Miller, H. F. Blichfeldt and L. E. Dickson, Theory and Applications of Finite Groups, NY, Stechert, 1938.

  18. L. Redei, Das "schiefe Produkt" in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungzahlen, zu denen nur kommutative Gruppen gehören, Comment. Math. Helvet. 20 (1947), 225-267.
    MathSciNet


Glasnik Matematicki Home Page