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Finite nonabelian p-groups having exactly one maximal subgroup with a noncyclic center

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Abstract

We prove here that a nonabelian finite p-group G has exactly one maximal subgroup with a noncyclic center if and only if Z(G) is cyclic and G has exactly one normal abelian subgroup of type (p, p).

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References

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

  2. Y. Berkovich, Groups of Prime Power Order, Volume 1, Walter de Gruyter, Berlin-New York, 2008.

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  1. Mathematical Institute, University of Heidelberg, 69120, Heidelberg, Germany

    Zvonimir Janko

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  1. Zvonimir Janko
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Correspondence to Zvonimir Janko.

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Janko, Z. Finite nonabelian p-groups having exactly one maximal subgroup with a noncyclic center. Arch. Math. 96, 101–103 (2011). https://doi.org/10.1007/s00013-010-0212-3

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  • DOI: https://doi.org/10.1007/s00013-010-0212-3

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