Glasnik Matematicki, Vol. 50, No. 1 (2015), 101-161.

CLASSIFICATION OF FINITE p-GROUPS WITH CYCLIC INTERSECTION OF ANY TWO DISTINCT CONJUGATE SUBGROUPS

Zvonimir Janko

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

Abstract.   We give a complete classification of non-Dedekindian finite p-groups in which any two distinct conjugate subgroups have cyclic intersection (Theorems A, B and C).

2010 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite p-groups, 2-groups of maximal class, Dedekindian p-groups, ordinary quaternion group, maximal non-normal subgroups, conjugate subgroups.

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DOI: 10.3336/gm.50.1.08

References:

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

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

  3. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 3, Walter de Gruyter, Berlin-New York, 2011.
    MathSciNet     CrossRef

  4. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 4, Walter de Gruyter, Berlin-New York, to appear 2014.
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