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The subgroups of Finite Metacyclic Groups

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Chinese Annals of Mathematics,Series B 2020年第2期41卷 241-266页

作者： Xu YANG School of Mathematical Sciences Fudan UniversityShanghai 200433China

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.

关键词： Metacyclic groups subgroups Metacyclic p-groups Characteristic subgroups

subgroups of chronic fatigue syndrome based on psychiatric disorder onset and current psychiatric status

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Health 2010年第2期2卷 90-96页

作者： Molly M. Brown Carly Kaplan Leonard A. Jason Christopher B. Keys Center for Community Research DePaul University

Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairment was ex-plored with a sample of 113 participants with CFS. subgroups were created based on past and current psychiatric status including those whose psychiatric history was premorbid and current, postmorbid and current, past but not current, and those with no lifetime diagnosis. Results from a one-way MANOVA revealed that patients with a premorbid and current psychiat-ric disorder reported significantly higher pain severity, more somatic symptoms, poorer sleep quality, and poorer quality of life than those with no psychiatric history. Levels of fatigue and physical functioning among patients with CFS were unrelated to the four subgroups in this study. Although those with a premorbid and current psychiatric disorder were differentiated from those with no psychiatric history on some markers of impairment, the sample as a whole had severe fatigue-related impairment, which is the cardinal symptom of CFS. Implications for research are discussed.

关键词： Chronic Fatigue Syndrome Psychiatric Comorbidity subgroups Impairment

Discreteness Criterion for subgroups in PU（1,n;C）

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Chinese Quarterly Journal of Mathematics 2018年第2期33卷 194-198页

作者： YANG Juan WANG hua School of Mathematics Sciences Kaili University Kaili 556000 Guizhou P.R.of China School of Mathematics and Computing Science Changsha University of Science and Technology Changsha410077 Hunan P.R.of China

In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.

关键词： Discreteness criterion n-dimensional subgroups PU(1,n C)

On s＊-Completions of Maximal subgroups of Finite Groups

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Chinese Quarterly Journal of Mathematics 2015年第3期30卷 381-388页

作者：高辉高胜哲尹丽 School of Science Dalian Ocean University

Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subg... 详细信息

关键词： maximal subgroups θ＊-completions s＊-completions solvable groups super-solvable groups

The influence of X-semipermutability of subgroups on the structure of finite groups

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Science China Mathematics 2009年第2期52卷 261-271页

作者： CHEN GuiYun LI JinBao School of Mathematics and Statistics Southwest UniversityChongqing 400715China School of Mathematical Sciences Xuzhou Normal UniversityXuzhou 221116China

Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained.

关键词： finite groups X-semipermutable subgroups supersoluble groups p-nilpotent groups subnormal subgroups Sylow subgroups cyclic subgroups

The Iwasava decomposition and intermediate subgroups of the Steinberg groups over the field of fractions of a principal ideal ring

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Science China Mathematics 2009年第2期52卷 318-322页

作者： MOISEENKOVA T. V. NUZHIN Ya. N. Institute of Fundamental Development Siberian Federal University St. Kirenskogo 26Krasnoyarsk 660074Russia

The Iwasava decomposition is proved for the Steinberg groups of types 2A2l-1, 2Dl, 2E6, 3D4 over the field of fractions of a principal ideal ring. By using this decomposition, it is described that subgroups exist betw... 详细信息

关键词： principal ideal ring Steinberg group intermediate subgroups

The influence of s-conditionally permutable subgroups on finite groups

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Science China Mathematics 2009年第2期52卷 301-310页

作者： LI BaoJun ZHANG ZhiRang School of Mathematics Chengdu University of Information TechnologyChengdu 610225China

A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, som... 详细信息

关键词： s-conditionally permutable subgroups supersoluble groups finite groups saturated formations

On finite 2-groups all of whose subgroups are mutually isomorphic

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Science China Mathematics 2009年第2期52卷 254-260页

作者： EPULIC Vladimir Faculty of Electrical Engineering and Computing University of Zagreb

In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabelian maximal subgroups. After that, we investigate the structure of isomaximal groups of order less than 64. Finally, in Theorem 14. we show that the minimal nonmetacyclic group of order 32 possesses a unique isomaximal extension of order 64.

关键词： p-groups maximal subgroups minimal nonabelian minimal nonmetacyclic

ON THE BOREL subgroups OF LARGE TYPE

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Chinese Annals of Mathematics,Series B 1992年第4期13卷 440-454页

作者：侯自新 Department of Mathematics Nankai University Tianjin 300071 China.

The author defines the large type Borel subgroups of a reductive algebraic group, which are used to discuss Langlands’ L-groups and the Langlands classification of the admissible representations of reductive algebraic groups over R (see [1, 2, 5])and determine all of the Borel subgroups of large type for the classical semisimple Lie groups.

关键词： Borel subgroups algebraic imaginary reductive admissible maximal verify trivial diagonal