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| 1 | Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ)显示文摘We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich. | AN LiJian LI LiLi QU HaiPeng ZHANG QinHai | 2014 | Science China Mathematics2014，57，4： | 9 |
| 2 | Finite p-Groups in Which the Number of Subgroups of Possible Order Is Less Than or Equal to p^3显示文摘In this paper, groups of order pn in which the number of subgroups of possible order is less than or equal to p3 are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order pn in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order pn with a cyclic subgroup of index p2 are the same. | Haipeng QU Ying SUN Qinhai ZHANG | 2010 | Chinese Annals of Mathematics,Series B2010，31，4： | 7 |
| 3 | Finite p-groups with a minimal non-abelian subgroup of index p(Ⅲ)显示文摘This paper finishes the classification of three-generator finite p-groups G such that Φ(G) Z(G).This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly solves a problem proposed by Berkovich(2008). | QU HaiPeng XU MingYao AN LiJian | 2015 | Science China Mathematics2015，58，4： | 6 |
| 4 | On Hua-Tuan's conjecture显示文摘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. | ZHANG QinHai & QU HaiPeng School of Mathematics and Computer Sciences, Shanxi Normal University, Linfen 041004, China | 2009 | Science China Mathematics2009，52，2： | 5 |
| 5 | Finite p-groups whose nonnormal subgroups are metacyclic显示文摘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 classified up to isomorphism.This solves a problem proposed by Berkovich. | Qiangwei Song Haipeng Qu | 2020 | Science China Mathematics2020，63，7： | 2 |
| 6 | On Hua-Tuan's conjecture Ⅱ显示文摘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. | ZHANG QinHai QU HaiPeng | 2011 | Science China Mathematics2011，54，1： | 2 |
| 7 | Finite p-Groups with Few Non-major k-Maximal Subgroups显示文摘A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G.In this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p^2 and δ_(d(G)-1)(G) = 0,respectively. | Boyan WEI Haipeng QU Yanfeng LUO | 2018 | Chinese Annals of Mathematics,Series B2018，39，1： | 1 |
| 8 | Generating long-wavelength absorption bands with enhanced deep red fluorescence and photothermal performance in fused carbon dots aggregates显示文摘Carbon dots(CDs)with long-wavelength absorptions and emissions are highly desired for biological applications.Herein,we report a new supra-CDs strategy to construct long-wavelength absorption bands based on fused CDs aggregates(f-CDAs)through a concentration-induced interparticle dehydration process among green emissive CDs(r-CDs)under solvothermal treatment.The obtained fused f-CDAs exhibit an obvious absorption band in 550-700 nm and significantly enhanced deep red fluorescence in N,N-dimethylformamide with photoluminescence quantum yields of 15.6% and high photothermal conversion efficiency up to 26.1%in water.Benefiting from the high photothermal performance,in vivo tumor photothermal therapy has been realized via intratumoral injection of f-CDAs under 655 nm laser irradiated at 0.5 W/cm^(2). | Jun Wu Josh Haipeng Lei Bingchen He Chu-Xia Deng Zikang Tang Songnan Qu | 2021 | Aggregate2021，2，6： | 1 |
| 9 | One step synthesis of efficient red emissive carbon dots and their bovine serum albumin composites with enhanced multi-photon fluorescence for in vivo bioimaging显示文摘Efficient red emissive carbon dots(CDs)in aqueous solutions are very scarce for high performance bioimaging applications.In this work,we report a one-step solvothermal treatment to synthesize pure red emissive CDs(FA-CDs)from citric acid and urea in formic acid without complicated purification procedures.Photoluminescence quantum yield(PLQY)of 43.4%was observed in their dimethyl sulfoxide solutions.High PLQY up to 21.9%in aqueous solutions was achieved in their bovine serum albumin(BSA)composites(FA-CDs@BSA)with significantly enhanced multiphoton fluorescence.The strong surface electron-withdrawing structure of FA-CDs caused by the high content of C=O groups contributes for their pure red emission.Owing to the significantly enhanced single and multi-photon red fluorescence and enlarged particle sizes after composing with BSA,in vivo tumor imaging and two-photon fluorescence imaging of blood vessels in mouse ear have been realized via intravenous injection of FA-CDs@BSA aqueous solutions. | Huiqi Zhang Gang Wang Zhiming Zhang Josh Haipeng Lei Tzu-Ming Liu Guichuan Xing Chu-Xia Deng Zikang Tang Songnan Qu | 2022 | Light(Science & Applications)2022，11，5： | 0 |
| 10 | Finite p-groups all of whose maximal abelian subgroups are soft显示文摘A subgroup A of a p-group G is said to be soft in G if CG(A) = A and |NG(A)/A| = p. In this paper we determined finite p-groups all of whose maximal abelian subgroups are soft; see Theorem A and Proposition 2.4. | QU HaiPeng Department of Mathematics, Shanxi Normal University, Linfen 041004, China | 2010 | Science China Mathematics2010，53，11： | 0 |
| 11 | Determining Sets and Determining Numbers of Finite Groups显示文摘A subset D of a group G is a determining set of G if every automorphism of G is uniquely determined by its action on D,and the determining number of G,a(G),is the cardinality of a smallest determining set.A group G is called a DEG-group if α(G)equals(G),the generating number of G.Our main results are as follows.Finite groups with determining number 0 or 1 are classified;finite simple groups and finite nilpotent groups are proved to be DEG-groups;for a given finite group H,there is a DEG-group G such that H is isomorphic to a normal subgroup of G and there is an injective mapping from the set of all finite groups to the set of finite DEG-groups;for any integer k≥2,there exists a group G such that α(G)=2 and(G)≥k. | Dengyin Wang Chi Zhang Haipeng Qu | 2024 | Algebra Colloquium2024，31，1： | 0 |
| 12 | Finite p-Groups G with H'=G'for Each A2-Subgroup H^(*)显示文摘A finite p-group G is called an At-group if t is the minimal non-negative integer such that all subgroups of index pt of G are abelian.The finite p-groups G with H'=G'for all A2-subgroups H of G are classified completely in this paper.As an application,a problem proposed by Berkovich is solved. | Dandan Zhang Haipeng Qu Yanfeng Luo | 2023 | Algebra Colloquium2023，30，2： | 0 |
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