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A generalized CAP-subgroup of a finite group

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Science China Mathematics 2015年第10期58卷 2133-2144页

作者： GUO WenBin SKIBA Alexander N. YANG NanYing School of Mathematical Sciences University of Science and Technology of China Department of Mathematics Francisk Skorina Gomel State University School of Science Jiangnan University

Let A be a subgroup of a finite group G. We say that A is a generalized CAP-subgroup of G if for each chief factor H/K of G either A avoids H/K or the following holds:(1) If H/K is non-abelian, then|H :(A ∩H)K | is a p′-number for every p ∈π((A ∩H)K/K);(2) If H/K is a p-group, then |G : NG(K(A ∩H))| is a p-number. In this paper, we use the generalized CAP-subgroup to characterize the structure of finite *** new characterizations of the hypercyclically embedded subgroups of a finite group are obtained and a series of known results are generalized.

关键词： finite group generalized CAP-subgroup U-embedded subgroup solubly saturated formation p-nilpotent group supersoluble subgroup

Some Sufficient Conditions on the Number of Non-abelian Subgroups of a finite group to be Solvable

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Acta Mathematica Sinica,English Series 2011年第5期27卷 891-896页

作者： Jiang Tao SHI Cui ZHANG LMAM & School of Mathematical Sciences Peking University Beijing 100871 P. R. China University of Primorska FAMNIT Glagoljaska 8 6000 Koper Slovenia University of Primorska PINT Muzejski trg 2 6000 Koper Slovenia

Thompson＇s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson＇s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.

关键词： finite group abelian subgroup solvable group

An Arithmetical Condition on the Sizes of Conjugacy Classes of a finite group

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Algebra Colloquium 2022年第3期29卷 375-384页

作者： Yongcai Ren School of Mathematics Sichuan UniversityChengdu 610064China

An element x of a finite group G is said to be primary if the order of x is a prime *** define csp2(G)as follows:if|x^(G)|is a prime power for every primary element x of G,where x^(G) is the conjugacy class of x in G,then csp2(G)=0;if there exists a primary element x in G such that|x^(G)|is divisible by at least two distinct primes,then csp2(G)=max{|x^(G)||x∈Gis primary,|x^(G)|is divisible by at least two distinct primes}.In this paper we discuss the influence of the number csp2(G)on the structure of G.

关键词： finite group primary element conjugacy class size solvable

On f-Hypercentral Actions of finite group

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Communications in Mathematics and Statistics 2021年第4期9卷 521-533页

作者： Baojun Li Lu Gong School of Sciences Nantong UniversityNantong 226019JiangsuPeople’s Republic of China

Let f be a formation function and G an *** is said that A acts f-hypercentrally on G if A acts f-centrally on every A-composition factor of *** this paper,groups are investigated by f-hypercentral *** particular,some ... 详细信息

关键词： finite group Formation f-hypercentral action Nilpotency

On X-s-Permutable Subgroups of a finite group

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Journal of Mathematical Research and Exposition 2010年第5期30卷 876-882页

作者： Min Bang SU Yang Ming LI Department of Mathematics Foshan University Guangdong 528000 P. R. China Department of Mathematics Guangdong University of Education Guangdong 510310 P. R. China

Let X be a nonempty subset of a group G. A subgroup H of G is said to be X- s-permutable in G if there exists an element x E X such that HP^x = P^xH for every Sylow subgroup P of G. In this paper, some new results are... 详细信息

关键词： finite group X-s-permutable subgroup the generalized Fitting subgroup formation.

finite groupS WHOSE AUTOMORPHISM group HAS ORDER CUBEFREE

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Chinese Annals of Mathematics,Series B 1997年第3期18卷 301-308页

作者： LI SHIRONG Department of Mathematics Guangxi UniversityNanning 530004China

LetGdenote a finite *** is shown that if|Aut(G)|is cubefree thenGpossesses the Sylow tower property.

关键词： finite group Automorphism group Sylow tower property

finite groups Isospectral to Simple groups

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Communications in Mathematics and Statistics 2023年第2期11卷 169-194页

作者： Maria A.Grechkoseeva Victor D.Mazurov Wujie Shi Andrey V.Vasil’ev Nanying Yang Sobolev Institute of Mathematics Koptyuga 4NovosibirskRussia 630090 Department of Mathematics Chongqing University of Arts and SciencesChongqing 402160People’s Republic of China School of Mathematics Suzhou UniversitySuzhou 215006People’s Republic of China School of Science Hainan UniversityHaikou 570228HainanPeople’s Republic of China School of Science Jiangnan UniversityWuxi 214122People’s Republic of China

The spectrum of a finite group is the set of element orders of this *** main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum,in particular,to list all finite simple g... 详细信息

关键词： finite group Simple group Element order Spectrum Recognition by spectrum

finite groups Acting 2-Transitively on Their Sylow Subgroups

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Acta Mathematica Sinica,English Series 1999年第1期15卷 131-144页

作者： Caiheng LiDepartment of Mathematics,the University of Western Australia,Nedlands,WA,6907,AustraliaJie WangDepartment of Mathematics,Peking University,Beijing 100871,P.R.China Department of Mathematics the University of Western Australia Nedlands Australia Department of Mathematics Peking University Beijing P. R. China

In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T.(3)all finite groups which are 2-transitive on all their sets of Sylow subgroups.

关键词： finite group Sylow subgroup 2-transitive action

finite groups with Four Relative Commutativity Degrees

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Algebra Colloquium 2015年第3期22卷 449-458页

作者： A. Erfanian M. Farrokhi D.G. Department of Pure Mathematics and Center of Excellence in Analysison Algebraic Structures Ferdowsi University of Mashhad Mashhad Iran Department of Pure Mathematics Ferdowsi University of Mashhad Mashhad Iran

It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel and complement isomorphic to Zp × Zp and Zq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.

关键词： relative commutativity degree commutativity degree finite group