Glasnik Matematicki, Vol. 45, No.2 (2010), 441-452.

FINITE p-GROUPS G WITH p>2 AND d (G)=2 HAVING EXACTLY ONE MAXIMAL SUBGROUP WHICH IS NEITHER ABELIAN NOR MINIMAL NONABELIAN

Zvonimir Janko

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

Abstract.   We give here a complete classification (up to isomorphism) of the title groups (Theorem 1 and Theorem 2). The corresponding problem for p=2 was solved in [4].

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Minimal nonabelian p-groups, A2-groups, metacyclic p-groups, Frattini subgroups, Hall-Petrescu formula, generators and relations.

Full text (PDF) (free access)

DOI: 10.3336/gm.45.2.11

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-New York, to appear 2011.

  4. Z. Božikov and Z. Janko, Finite 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian, Glas. Mat. Ser. III 45(65) (2010), 63-83.
    CrossRef
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