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Finite p-groups in which the number of subgroups of possible order is less than or equal to p 3

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Abstract

In this paper, groups of order p n in which the number of subgroups of possible order is less than or equal to p 3 are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order p n in which the number of subgroups of possible order is less than or equal to p 3 and the classification of groups of order p n with a cyclic subgroup of index p 2 are the same.

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Authors and Affiliations

  1. Department of Mathematics, Shanxi Normal University, Linfen, 041004, Shanxi, China

    Haipeng Qu, Ying Sun & Qinhai Zhang

Authors
  1. Haipeng Qu
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  2. Ying Sun
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  3. Qinhai Zhang
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Corresponding author

Correspondence to Qinhai Zhang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10671114), the Shanxi Provincial Natural Science Foundation of China (No. 2008012001) and the Returned Abroad-Student Fund of Shanxi Province (No. [2007]13-56).

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Qu, H., Sun, Y. & Zhang, Q. Finite p-groups in which the number of subgroups of possible order is less than or equal to p 3 . Chin. Ann. Math. Ser. B 31, 497–506 (2010). https://doi.org/10.1007/s11401-010-0590-7

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  • DOI: https://doi.org/10.1007/s11401-010-0590-7

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