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finite groups with Seminormal Sylow Subgroups

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Acta Mathematica Sinica,English Series 2008年第10期24卷 1751-1757页

作者： Wen Bin GUO Department of Mathematics Xuzhou Normal University Xuzhou 221116 P. R. China Department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China

In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G）／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.

关键词： finite groups seminormal subgroups Sylow subgroups p-soluble groups p-supersoluble groups

On Existence of Hall Subgroups in finite groups

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Algebra Colloquium 2017年第1期24卷 75-82页

作者： Yufeng Liu Wenbin Guo N. Skiba School of Mathematics and Informational ScienceShandong Institute of Business and Technology Yantai Shandong 264005 China School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026 China Department of Mathematics Gomel State University of F. Skorina Gomel 246028 Belarus

In this paper, we give some new conditions of the existence of Hall subgroups in non-soluble finite groups, and so the famous Hall theorem and Schur-Zassenhaus theorem are generalized.

关键词： finite groups non-soluble groups Hall subgroups

Criteria of Existence of Hall Subgroups in Non-soluble finite groups

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Acta Mathematica Sinica,English Series 2010年第2期26卷 295-304页

作者： Wen Bin GUO A. N. SKIBA Department of Mathematics Xuzhou Normal University Xuzhou 221116 P. R. China Department of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus

In this paper, the famous Hall theorem and the famous Schur-Zassenhaus theorem are generalized.

关键词： finite groups non-soluble groups Hall subgroups

Special Blocks of finite groups

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Acta Mathematica Sinica,English Series 2016年第1期32卷 115-123页

作者： Ji Ping ZHANG Beijing International Center for Mathematical Research Lmam School of Mathematical SciencesPeking University

We first determine in this paper the structure of the generalized Fitting subgroup F＊（G） of the finite groups G all of whose defect groups （of blocks） are conjugate under the automorphism group Aut（G） to either a Sylow p-subgroup or a fixed p-subgroup of G. Then we prove that if a finite group L acts transitively on the set of its proper Sylow p-intersections, then either L/Op（L） has a T.I. Sylow p-subgroup or p = 2 and the normal closure of a Sylow 2-subgroup of L/O2（L） is 2-nilpotent with completely descripted structure. This solves a long-open problem. We also obtain some generalizations of the classic results by Isaacs and Passman on half-transitivity.

关键词： finite groups representations blocks defect groups

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Algebra Colloquium 2020年第2期27卷 193-198页

作者： S.M.Robati Department of Mathematics Faculty of Science Imam Khomeini International UniversityQazvinIran

Let G be a group,and let →/ΓC(G) be a digraph whose vertices are the nontrivial conjugacy classes of G and there is an arc from a vertex C to a vertex C' if and only if C≠C' and(C)■(C').In this paper,we characteri... 详细信息

关键词： conjugacy classes posets graphs finite groups

ON F-z-SUPPLEMENTED SUBgroups OF finite groups

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Acta Mathematica Scientia 2011年第1期31卷 22-28页

作者：郭文彬唐娜李保军 Department of Mathematics University of Science and Technology of China Department of Mathematics Xuzhou Normal University Department of Mathematics Huaiyin Teachers College School of Mathematics Chengdu University of Information Technology

A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-suppl... 详细信息

关键词： finite groups local formations F-z-supplemented subgroups supersoluble groups p-nilpotent groups

finite groups With Small Automizers for Their Nonabelian Subgroups

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数学进展 1998年第4期27卷 86-87页

作者：吕克伟北京大学数学系北京

Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ，Ｇｉｓａｆｉｎｉｔｅｇｒｏｕｐ．ＳｅｔＡｕｔＧ（Ｈ）＝ＮＧ（Ｈ）／ＣＧ（Ｈ）ｆｏｒＨ≤Ｇ．Ｉｎ［ＤＭ］，ａｕｔｈｏｒｓｇａｖｅｔｈｅｆｏｌｏｗｉｎｇｄｅｆｉｎｉｔｉｏｎｓ：（１... 详细信息

Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ，Ｇｉｓａｆｉｎｉｔｅｇｒｏｕｐ．ＳｅｔＡｕｔＧ（Ｈ）＝ＮＧ（Ｈ）／ＣＧ（Ｈ）ｆｏｒＨ≤Ｇ．Ｉｎ［ＤＭ］，ａｕｔｈｏｒｓｇａｖｅｔｈｅｆｏｌｏｗｉｎｇｄｅｆｉｎｉｔｉｏｎｓ：（１）ＬｅｔＨ≤Ｇ，ＡｕｔＧ（Ｈ）＝Ｎ...

关键词： finite groups With Small Automizers Their Nonabelian Subgroups

finite groups Whose Nontrivial Normal Subgroups Have Order Two

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Journal of Mathematical Research and Exposition 2011年第4期31卷 675-680页

作者： Shou Hong QIAO Da Chang GUO School of Applied Mathematics Guangdong University of Technology Guangdong 510006 P. R. China

In this paper, we investigate the structure of the groups whose nontrivial normal subgroups have order two. Some properties of this kind of groups are obtained.

关键词： finite groups normal subgroups soluble groups insoluble groups simple groups

finite groups with Some Subgroups Weakly s-Permutably Embedded

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Journal of Mathematical Research with Applications 2014年第5期34卷 535-542页

作者： Shouhong QIAO Yanming WANG School of Applied Mathematics Guangdong University of Technology Lingnan College and School of Mathematics Sun Yat-sen University

Let P be a Sylow p-subgroup of a group G with the smallest generator number d,where p is a *** by M;（P） = {P;,P;P;} a set of maximal subgroups of P such that φ（P） = ∩;P;.In this paper,we investigate the structure of a finite group G under the assumption that the maximal subgroups in M;（P） are weakly s-permutably embedded in G,some interesting results are obtained which generalize some recent ***,we give some further results in terms of weakly s-permutably embedded subgroups.

关键词： finite groups weakly s-permutably embedded subgroups p-nilpotent groups p-supersolvable groups supersolvable groups.