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Finite p-groups whose nonnormal subgroups are metacyclic

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Abstract

For an odd prime p, we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic, and based on the criterion, the p-groups whose nonnormal subgroups are metacyclic are classifid up to isomorphism. This solves a problem proposed by Berkovich.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11771258 and 11471198). The authors thank Professor Qinhai Zhang for his helpful suggestions.

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Authors and Affiliations

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

    Qiangwei Song & Haipeng Qu

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  1. Qiangwei Song
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  2. Haipeng Qu
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Correspondence to Haipeng Qu.

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Song, Q., Qu, H. Finite p-groups whose nonnormal subgroups are metacyclic. Sci. China Math. 63, 1271–1284 (2020). https://doi.org/10.1007/s11425-018-9479-1

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  • DOI: https://doi.org/10.1007/s11425-018-9479-1

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