Glasnik Matematicki, Vol. 52, No. 1 (2017), 99-105.

FINITE NONABELIAN p-GROUPS OF EXPONENT >p WITH A SMALL NUMBER OF MAXIMAL ABELIAN SUBGROUPS OF EXPONENT >p

Zvonimir Janko

Abstract.   Y. Berkovich has proposed to classify nonabelian finite p-groups G of exponent >p which have exactly p maximal abelian subgroups of exponent >p and this was done here in Theorem 1 for p=2 and in Theorem 2 for p>2. The next critical case, where G has exactly p+1 maximal abelian subgroups of exponent >p was done only for the case p=2 in Theorem 3.

2010 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite p-groups, minimal nonabelian subgroups, maximal abelian subgroups, quasidihedral 2-groups, Hughes subgroup.

DOI: 10.3336/gm.52.1.07

References:

1. Y. Berkovich, Groups of prime power order, Vol. 1, Walter de Gruyter, Berlin-New York, 2008.
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2. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 2, Walter de Gruyter, Berlin-New York, 2008.
   MathSciNet    

3. Z. Janko, Finite p-groups with some isolated subgroups, J. Algebra 465 (2016), 41-61.
   MathSciNet     CrossRef