Glasnik Matematicki, Vol. 40, No.2 (2005), 235-240.

FINITE p-GROUPS WITH A UNIQUENESS CONDITION FOR NON-NORMAL SUBGROUPS

Zvonimir Janko

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


Abstract.   We determine up to isomorphism all finite p-groups G which possess non-normal subgroups and each non-normal subgroup is contained in exactly one maximal subgroup of G. For p = 2 this problem was essentially more difficult and we obtain in that case two new infinite families of finite 2-groups.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite p-groups, minimal nonabelian p-groups, 2-groups of maximal class, Hamiltonian groups.


Full text (PDF) (free access)

DOI: 10.3336/gm.40.2.04


References:

  1. B. Huppert, Endliche Gruppen 1, Springer, Berlin, 1967.

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