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On Hua-Tuan’s conjecture

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【Author】 ZHANG QinHai & QU HaiPeng School of Mathematics and Computer Sciences, Shanxi Normal University, Linfen 041004, China

【摘要】 Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have 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). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold.更多还原

【Abstract】 Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have 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). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold.更多还原

【关键词】 Hua-Tuan’s conjecture； metacyclic p-groups； abelian p-groups； inner abelian p- groups； superspecial p-groups；
【Key words】 Hua-Tuan’s conjecture； metacyclic p-groups； abelian p-groups； inner abelian p- groups； superspecial p-groups；

【基金】 supported by National Natural Science Foundation of China (Grant No. 10671114);the Natural Science Foundation of Shanxi Province (Grant No. 2008012001);the Returned Abroad-Student Fund of Shanxi Province (Grant No. [2007]13-56)

【文献出处】 Science in China(Series A:Mathematics) ,中国科学(A辑:数学)(英文版) , 编辑部邮箱 ,2009年02期

【分类号】O152.1
【被引频次】6
【下载频次】34

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