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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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Science China Mathematics 2024年第9期67卷 1989-2018页

作者： Yulei Wang heguo liu Department of Mathematics Henan University of TechnologyZhengzhou 450001China Department of Mathematics Hainan UniversityHaikou 570228China

Let p be a prime and F be a finite field of characteristic *** that FG is the group algebra of the finite p-group G over the field *** 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 *** 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≥***,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}.

关键词： normalized unit unitary subgroup inner abelian p-group central extension

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新形势下商品住宅质量投诉热点分析

工程质量 2024年第5期42卷 82-84页

作者：刘和国南京市建筑工程质量安全监督站江苏南京210007

随着房地产形势持续下行,商品住宅质量难以保障,人民群众反应日益强烈。论文梳理分析某地区商品房质量投诉热点及产生原因,给出预防性建议,可供工程质量监督人员及项目质量管理人员参考,为从技术角度提升商品住宅工程质量带来新思考。

关键词：商品住宅质量投诉质量管理

Automorphism Groups of Some Finite p-Groups

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Algebra Colloquium 2016年第4期23卷 623-650页

作者： heguo liu Yulei Wang Department of Mathematics Hubei University Wuhan 430062 China Department of Mathematics Henan University of Technology Zhengzhou 450001 China

The automorphism group of G is determined, where G is a nonabelian p-group given by a central extension as 1→Zpm→G→Zp×…×Zp→1 such that its derived subgroup has order p.

关键词： generalized extraspecial p-group symplectic space orthogonal space auto-morphism central extension

On Non-commuting Sets in Certain Finite p-Groups

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Algebra Colloquium 2015年第4期22卷 555-560页

作者： heguo liu Yulei Wang Department of Mathematics Hubei University Wuhan 430062 China vDepartment of Mathematics Henan University of Technology Zhengzhou 450001 China

Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group G is determined, where G is a non-abelian p-group given by a central extension as1 → Zp→ G →Zp ×→ × Zp →1 and its derivedsubgroup has order p.

关键词： generalized extraspecial p-group central product non-commuting set

关于Seksenbaev-Robinson定理

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数学年刊（A辑） 2024年第2期45卷 185-204页

作者：刘合国张继平赵静徐行忠廖军海南大学数学与统计学院海口570228 北京大学数学科学学院北京100871 海南省工程建模与统计计算重点实验室海口570228 湖北大学数学与统计学学院武汉430062

剩余有限群也被称为是可以有限逼近的群,其特性常常由它的有限商群的性质决定.Seksenbaev定理断言:若对无限多个素数p,多重循环群G都是剩余有限p-群,则G是有限生成的无挠幂零群.Robinson把该定理推广为:设G是有限秩的可解群,若对无限多... 详细信息

剩余有限群也被称为是可以有限逼近的群,其特性常常由它的有限商群的性质决定.Seksenbaev定理断言:若对无限多个素数p,多重循环群G都是剩余有限p-群,则G是有限生成的无挠幂零群.Robinson把该定理推广为:设G是有限秩的可解群,若对无限多个素数p,G都是剩余有限p-群,则G是有限秩的无挠幂零群.这是无限可解群里的两个经典结果.本文证明了有关无限可解群的两个剩余有限性定理.本文的结果完善了Seksenbaev-Robinson定理.

关键词：可解群剩余有限性不可约多项式整群环下中心列

The Automorphism Group of a Finite p-Group with a Cyclic Frattini Subgroup

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 613-642页

作者： heguo liu Yulei WANG Department of Mathematics Hubei UniversityWuhan 430062China Department of Mathematics Henan University of TechnologyZhengzhou 450001China

Let G be a finite p-group with a cyclic Frattini subgroup. In this paper, the automorphism group of G is determined.

关键词： Finite p-groups Frattini subgroups Automorphisms

Regular automorphisms of order p2

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Frontiers of Mathematics in China 2019年第6期14卷 1367-1373页

作者： Tao XU heguo liu Department of Science Hebei University of EngineeringHandan 056038China Department of Mathematics Hubei UniversityWuhan 430062China

Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a *** G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is *** G is polycyclic,then CG(a^p)and G/[... 详细信息

关键词： Polycyclic group regular automorphism residually finite

On the Residual Finiteness of a Class of Infinite Soluble Groups

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Algebra Colloquium 2023年第1期30卷 155-164页

作者： Jun Liao heguo liu Xiaoliang Luo Xingzhong Xu School of Mathematics and Statistics Hubei UniversityWuhan 430062China Department of Mathematics Hainan UniversityHaikou 570228China Department of Mathematics Taiyuan Normal University JinzhongShanxi 031609China

Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted b... 详细信息

关键词： residual finiteness infinite soluble group nilpotent group polycyclic group

Two Notes on Auto morphisms of Modules over a PID

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Algebra Colloquium 2019年第3期26卷 401-410页

作者： heguo liu Xiaoliang Luo Xin Qin Bomin Zan School of Mathematics and Statistics Hubei UniversityWuhan 430062China

Let Z>be a principal ideal domain(PID)and M be a module over *** prove the following two dual results:(i)If M is finitely generated and rr,y are two elements in M such that M/Dx≌M/Dy,then there exists an auto morphism a of M such that a(x)=y.(ii)If M satisfies the minimal cond计ion on submodules and X,Y are two locally cyclic submodules of M such that M/X≌M/Y and X≌Y,then there exists an automorphism a of M such that α(X)=Y.

关键词： auto morphism of modules finitely generated module module with minimumcondition on submodules