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Finite p-groups whose nonnormal subgroups are metacyclic 被引量:2
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作者 Qiangwei Song Haipeng Qu 《Science China Mathematics》 SCIE CSCD 2020年第7期1271-1284,共14页
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.Thi... 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. 展开更多
关键词 metacyclic groups minimal nonabelian groups minimal nonmetacyclic groups p-groups of maximal class the rank of a p-group
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内亚循环capable群性质研究 被引量:1
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作者 李志秀 《山东科学》 CAS 2015年第5期77-79,共3页
本文研究了内亚循环p-群G满足capable群的条件,得到了这类群为capable p-群的充要条件。并由内亚循环p-群G构造得出了群H,满足H/Z(H)同构于G。
关键词 capable群 内亚循环群
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非平凡子群皆自中心化的有限群(英文) 被引量:1
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作者 张良才 陈顺民 《喀什师范学院学报》 2002年第3期21-23,共3页
群G的子群H称为G的自中心化子群,若CG(H)≤H.刻划了非平凡子群皆自中心化的有限 群.
关键词 中心化子 自中心化子群 内幂零群 亚循环群
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Finite p-Groups in Which the Number of Subgroups of Possible Order Is Less Than or Equal to p^3 被引量:8
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作者 Haipeng QU Ying SUN Qinhai ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第4期497-506,共10页
In this paper, groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 ale classified. It turns out that if p 〉 2, n≥ 5, then the classification of groups of order p^n in w... In this paper, groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 ale classified. It turns out that if p 〉 2, n≥ 5, then the classification of groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order p^n with a cyclic subgroup of index p2 are the same. 展开更多
关键词 inner abelian p-groups metacyclic p-groups Groups of order p^n with a cyclic subgroup of index p^2 The number of subgroups
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Finite p-Groups Whose Subgroups of Given Order are Isomorphic and Minimal Non-abelian 被引量:1
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作者 Qinhai Zhang 《Algebra Colloquium》 SCIE CSCD 2019年第1期1-8,共8页
Finite p-groups whose subgroups of given order are isomorphic and minimal non-abelian are classified. In addition, two results on a chain condition of At-groups are improved.
关键词 metacyclic p-groups At-groups chain condition of At-groups
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The Subgroups of Finite Metacyclic Groups
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作者 Xu YANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2020年第2期241-266,共26页
In this paper, the author characterizes the subgroups of a finite metacyclic group K by building a one to one correspondence between certain 3-tuples(k, l, β) ∈ N3 and all the subgroups of K. The results are applied... In this paper, the author characterizes the subgroups of a finite metacyclic group K by building a one to one correspondence between certain 3-tuples(k, l, β) ∈ N3 and all the subgroups of K. The results are applied to compute some subgroups of K as well as to study the structure and the number of p-subgroups of K, where p is a fixed prime number. In addition, the author gets a factorization of K, and then studies the metacyclic p-groups, gives a different classification, and describes the characteristic subgroups of a given metacyclic p-group when p ≥ 3. A "reciprocity" relation on enumeration of subgroups of a metacyclic group is also given. 展开更多
关键词 metacyclic GROUPS SUBGROUPS metacyclic p-groups CHARACTERISTIC SUBGROUPS
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Finite 2-generator equilibrated p-groups
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作者 Qin-hai ZHANG Cui-juan SUN +1 位作者 Hai-peng QU Ming-yao XU 《Science China Mathematics》 SCIE 2007年第6期814-820,共7页
Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of met... Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of metacyclic p-groups given by Newman and Xu, we give a complete classification of 2-generator equilibrated p-groups in this note. 展开更多
关键词 equilibrated group metacyclic group finite p-group minimal non-abelian group 20D15
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The unitary subgroups of group algebras for a class of finite 2-groups with the derived subgroup of order 2
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作者 Yulei Wang Heguo Liu 《Science China Mathematics》 SCIE CSCD 2024年第9期1989-2018,共30页
Let p be a prime and F be a finite field of characteristic p.Suppose that FG is the group algebra of the finite p-group G over the field F.Let V(FG)denote the group of normalized units in FG and let V_(*)(FG)denote th... Let p be a prime and F be a finite field of characteristic p.Suppose that FG is the group algebra of the finite p-group G over the field F.Let V(FG)denote the group of normalized units in FG and let V_(*)(FG)denote the unitary subgroup of V(FG).If p is odd,then the order of V_(*)(FG)is|F|^((|G-1)/2).However,the case p=2 still is open.In this paper,the order of V*(FG)is computed when G is a nonabelian 2-group given by a central extension of the form 1→Z_(2^(n))×Z_(2^(m))→G→Z_(2)×…×Z_(2)→1 and G'≌Z_(2),n,m≥1.Furthermore,a conjecture is confirmed,i.e.,the order of V_(*)(FG)can be divisible by|F|^(1/2(|G|+|Ω1(G)|)-1),where Ω_(1)(G)={g∈G|g^(2)=1}. 展开更多
关键词 normalized unit unitary subgroup inner abelian p-group central extension
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用子群计数刻画有限p群 被引量:3
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作者 安立坚 刘一丁 《数学进展》 CSCD 北大核心 2011年第3期285-292,共8页
本文利用子群计数刻画了型不变量为(p^k,p,p,…,p)的交换p群以及亚循环的内交换p群(其中p为奇素数).
关键词 正则p群 内交换群 亚循环群
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满足|I_3(G)|=4的有限2群的完全分类 被引量:1
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作者 安立坚 魏军军 《数学的实践与认识》 CSCD 北大核心 2010年第22期237-242,共6页
完全分类了满足|I_3(G)|=4的有限2群,其中I_k(G)表示G的所有p^k阶子群的交.
关键词 内交换群 亚循环群 内亚循环群 Ti群
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On Hua-Tuan's conjecture 被引量:6
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作者 ZHANG QinHai & QU HaiPeng School of Mathematics and Computer Sciences, Shanxi Normal University, Linfen 041004, China 《Science China Mathematics》 SCIE 2009年第2期389-393,共5页
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 &g... 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. 展开更多
关键词 Hua-Tuan’s CONJECTURE metacyclic p-groups ABELIAN p-groups inner ABELIAN p- groups superspecial p-groups
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