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| On Hua-Tuan’s conjecture Ⅱ | |
| 基金项目： | supported by National Natural Science Foundation of China (Grant No.11071150); Natural Science Foundation of Shanxi Province (Grant No. 2008012001); The Returned Abroad-student Foundation of Shanxi Province (Grant No. [2007]13-56) |
| 摘 要： | Let G be a group of order pn, p a prime. For 0 m n, sm(G) denotes the number of subgroups of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan had ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1+p, 1+p+p2 or 1+p+2p2(mod p3). The conjecture has a negative answer. In this paper, we further investigate the conjecture and propose two new conjectures. |
| 关 键 词： | Hua-Tuan’s conjecture p-groups of maximal class enumeration of subgroups Magma package |
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