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On Hua-Tuan’s conjecture II

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Abstract

Let G be a group of order p n, p a prime. For 0 ⩽ m ⩽ n, s m (G) denotes the number of subgroups of order p m of G. Loo-Keng Hua and Hsio-Fu Tuan had ever conjectured: for an arbitrary finite p-group G, if p > 2, then s m (G) ≡ 1, 1+p, 1+p+p 2 or 1+p+2p 2(mod p 3). The conjecture has a negative answer. In this paper, we further investigate the conjecture and propose two new conjectures.

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Authors and Affiliations

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

    QinHai Zhang & HaiPeng Qu

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  1. QinHai Zhang
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  2. HaiPeng Qu
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Correspondence to QinHai Zhang.

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Zhang, Q., Qu, H. On Hua-Tuan’s conjecture II. Sci. China Math. 54, 65–74 (2011). https://doi.org/10.1007/s11425-010-4136-y

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  • DOI: https://doi.org/10.1007/s11425-010-4136-y

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