On Hua-Tuan’s conjecture II
On Hua-Tuan’s conjecture II
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DOI：
10.1007/s11425-010-4136-y
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发表时间：
2011-01
期刊：
影响因子：
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通讯作者：
Qinhai Zhang;H. Qu
中科院分区：
文献类型：
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作者：
Qinhai Zhang;H. Qu
LetGbe a group of orderpn,pa prime. For 0 ⩽m⩽n,sm(G) denotes the number of subgroups of orderpmofG. Loo-Keng Hua and Hsio-Fu Tuan had ever conjectured: for an arbitrary finitep-groupG, ifp> 2, thensm(G) ≡ 1, 1+p, 1+p+p2or 1+p+2p2(modp3). The conjecture has a negative answer. In this paper, we further investigate the conjecture and propose two new conjectures.
