Glasnik Matematicki, Vol. 46, No.2 (2011), 351-356.

FINITE p-GROUPS ALL OF WHOSE PROPER SUBGROUPS HAVE ITS DERIVED SUBGROUP OF ORDER AT MOST p

Zvonimir Janko

Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany
e-mail: janko@mathi.uni-heidelberg.de


Abstract.   We give in Theorem 7 a complete characterization of the title groups.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite p-groups, minimal nonabelian p-groups, commutator subgroups, nilpotency class of p-groups.


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DOI: 10.3336/gm.46.2.07


References:

  1. Y. Berkovich, Groups of prime power order, Vol. 1, Walter de Gruyter, Berlin, 2008.
    MathSciNet    

  2. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 2, Walter de Gruyter, Berlin, 2008.
    MathSciNet    

  3. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 3, Walter de Gruyter, Berlin, 2011.

  4. V. Ćepulić and O. Pylyavska, Determination of p-groups all of whose proper subgroups have a commutator subgroup of order equal or less than p (p≥ 3), Naukovi zapysky, Kyyevo 39 (2005), 28-34.

  5. J. Q. Zhang and X. H. Li, Finite p-groups all of whose proper subgroups have small derived subgroups, Sci. China Math. 53 (2010), 1357-1362.
    MathSciNet     CrossRef

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