Glasnik Matematicki, Vol. 44, No.1 (2009), 177-185.

A COMPLETE CLASSIFICATION OF FINITE p-GROUPS ALL OF WHOSE NONCYCLIC SUBGROUPS ARE NORMAL

Zdravka Božikov and Zvonimir Janko

Faculty of Civil Engineering and Architecture, University of Split, 21000 Split, Croatia
e-mail: Zdravka.Bozikov@gradst.hr

Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany

Abstract.   We give a complete classification of finite p-groups all of whose noncyclic subgroups are normal, which solves a problem stated by Berkovich.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Dedekindian p-groups, Hamiltonian 2-groups, minimal nonabelian p-groups, central products.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.1.10

References:

  1. Y. Berkovich, Groups of prime power order, I and II (with Z. Janko), Walter de Gruyter, 2008.
    MathSciNet

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

  3. B. Huppert, Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften 134, Springer-Verlag, Berlin-New York, 1967.
    MathSciNet

  4. Z. Janko, Finite 2-groups with exactly four cyclic subgroups of order 2n, J. Reine Angew. Math. 566 (2004), 135-181.
    MathSciNet     CrossRef

  5. 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

  6. D. S. Passman, Nonnormal subgroups of p-groups, J. Algebra 15 (1970), 352-370.
    MathSciNet     CrossRef

Glasnik Matematicki Home Page