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ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS 认领 引用 被引量：9
1
作者 郭文彬 唐娜 李保军 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期22-28,共7页
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... 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-supplemented subgroups and use them to determine the structure of some groups. 展开更多
关键词 Finite groups local formations F-z-supplemented subgroups supersoluble groups p-nilpotent groups
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Finite Groups with Some Subgroups Weakly s-Permutably Embedded 认领 引用
2
作者 Shouhong QIAO Yanming WANG 《Journal of Mathematical Research with Applications》 CSCD 2014年第5期535-542,共8页
Let P be a Sylow p-subgroup of a group G with the smallest generator number d, where p is a prime. Denote by Md（P） = （P1, P2,..., Pd） a set of maximal subgroups of P such that φ（P） = ∩n^d=1Pn. In this paper, w... Let P be a Sylow p-subgroup of a group G with the smallest generator number d, where p is a prime. Denote by Md（P） = （P1, P2,..., Pd） a set of maximal subgroups of P such that φ（P） = ∩n^d=1Pn. In this paper, we investigate the structure of a finite group G under the assumption that the maximal subgroups in Md（P） are weakly s-permutably embedded in G, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly s-permutably embedded subgroups. 展开更多
关键词 finite groups weakly s-permutably embedded subgroups p-nilpotent groups p-supersolvable groups supersolvable groups.
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Finite Groups Whose Norm Quotient Groups Have Cyclic Sylow Subgroups 认领 引用
3
作者 Songliang CHEN Yun FAN 《Journal of Mathematical Research with Applications》 CSCD 2022年第2期153-161,共9页
Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm q... Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm quotient group G/N(G)is cyclic;2)all Sylow subgroups of G/N(G)are cyclic and in particular if the order of G/N(G)is a square-free number. 展开更多
关键词 norm Dedekind group Hamiltonian group π-group structure of finite group Sylow subgroup
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Finite Groups with Only s-quasinormal and Abnormal Subgroups 认领 引用 被引量：2
4
作者 Zhang Qinhai 《Northeastern Mathematical Journal》 1998年第1期41-46,共6页
The concept of an abnormal subgroup of a group G is,in a sense,opposite of thatof a normal subgroup of G.In[J.Algebra,28(1974),15-19]Fattahi studied those finitegroups in which each subgroup is either normal or abnorm... The concept of an abnormal subgroup of a group G is,in a sense,opposite of thatof a normal subgroup of G.In[J.Algebra,28(1974),15-19]Fattahi studied those finitegroups in which each subgroup is either normal or abnormal and characterized all suchgroups.In this paper,as a generalization of Fattahi’s result,we study more general groups,i.e.,groups with only s-quasinormal and abnormal subgroups and characterize all suchgroups.Morever,some interesting conclusions are also obtained. 展开更多
关键词 Groups Finite Groups Abnormal Subgroups
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Finite Groups with Metacyclic Automorphism Groups 认领 引用
5
作者 Chen Guiyun Chigira Naoki +1 位作者 Yamaki Hiroyoshi Niu Fengwen 《Northeastern Mathematical Journal》 1998年第1期5-8,共4页
There is an interesting but difficult problem:Problem When a finite group Gis given,determine a finite group X with Aut(X)=G.The problem was discussed in several articles.Miller[1]determined all X with G=S3,G=S4... There is an interesting but difficult problem:Problem When a finite group Gis given,determine a finite group X with Aut(X)=G.The problem was discussed in several articles.Miller[1]determined all X with G=S3,G=S4and G=Zn,where Snis the symmetric group on n letters and Znis the cyclic group of order n. 展开更多
关键词 Finite Group Automorphism Group Structure of Group
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F-Decomposition of Minimax Module over Hyper Finite Groups 认领 引用
6
作者 秦应兵 盛晓玲 《Journal of Southwest Jiaotong University(English Edition)》 2008年第2期195-198,共4页
Let G be a hyper finite locally solvable group, A a minimax ZG-medule, a locally defined formation consisting of locally solvable groups, A has no nonzero infinite irreducible ZG-factors, and G ∈ . The following resu... Let G be a hyper finite locally solvable group, A a minimax ZG-medule, a locally defined formation consisting of locally solvable groups, A has no nonzero infinite irreducible ZG-factors, and G ∈ . The following results are proved： if A has a maximal submodule B such that A/B is , central in G and B has no nonzero central ZG-factors, then A has an decomposition; ifA has an irreducible central submodule B such that all ZG-composition factors of A/B are o^eccentric, then A has an decomposition. 展开更多
关键词 Minimax module Hyper finite group Decomposition
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More on the Set of Element Orders in Finite Groups 认领 引用
7
作者 Naoki Chigira Shi Wujie Niu Fengwen 《Northeastern Mathematical Journal》 1996年第3期6-9,共4页
Let G be a finite group.Denote by πe(G) the set of element orders of G,and for any subset m of positive integers denote by h(m)the number of isomorphic classes of G satisfying πe(G)=m.In[1],the authors made th... Let G be a finite group.Denote by πe(G) the set of element orders of G,and for any subset m of positive integers denote by h(m)the number of isomorphic classes of G satisfying πe(G)=m.In[1],the authors made the following conjecture:for all subsets m of positive integers,h(m)∈{0,1,∞}.Recently,Mazurov[2]proved the following result:If m=πe(L3(5)),then h(m)=2.Thus he gave a negative answer to the above conjecture.In this paper,we shall give another example with h(m)=2. 展开更多
关键词 Finite Simple Group Solvable Group Set of Element Orders
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Real and Quasi-central Elements of Finite Groups 认领 引用
8
作者 Huaquan Wei Yi Chen +2 位作者 Jiamin Zhang Hui Wu Xuanyou Hou 《Algebra Colloquium》 SCIE CSCD 2026年第1期15-22,共8页
An element x of a finite group G is said to be real in G if x y=x−1 for some y in G,and quasi-central if xy=x-1 for each y in G.When G is a 2-group,Ω1(G)≤Z(G)and G=Ω2 R(G),we prove that if every real eleme... An element x of a finite group G is said to be real in G if x y=x−1 for some y in G,and quasi-central if xy=x-1 for each y in G.When G is a 2-group,Ω1(G)≤Z(G)and G=Ω2 R(G),we prove that if every real element in G of order 4 is quasi-central in G,then every element c in G of order 4 is real andis normal in G.Further,we show that a group G with a Sylow p-subgroup P is p-nilpotent if and only if N G(P)is p-nilpotent and,for all x in G\N G(P),one of the following holds:(a)every element in P∩Px∩GNp of order p is quasi-central in P,and if p=2,every real element in P∩Px∩GNp of order 4 is quasi-central in P;(b)every element in P∩Px∩GNp of order p is quasi-central in P,and if p=2,[Ω2 R(P∩Px∩GNp),P]⊆Ω1(P∩GNp)∪Z(P∩GNp);(c)|ΩR(P∩Px∩GNp)|≤pp−1. 展开更多
关键词 finite group real element quasi-central element p-nilpotency
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SS-Quasinormal Subgroups and p-Nilpotency of Finite Groups 认领 引用
9
作者 Yong Xu 《Algebra Colloquium》 SCIE CSCD 2026年第2期319-326,共8页
For a nontrivial p-group P,a maximal chain of P is a chain of subgroups 1=P0■P1■···■Pn=P with|Pi:Pi−1|=p for i=1,2,...,n,where n is an integer.We determine the structure of finite grou... For a nontrivial p-group P,a maximal chain of P is a chain of subgroups 1=P0■P1■···■Pn=P with|Pi:Pi−1|=p for i=1,2,...,n,where n is an integer.We determine the structure of finite groups having SS-quasinormality of a maximal chain of Sylow subgroups.We obtain new characterizations of finite p-nilpotent groups and supersolvable groups. 展开更多
关键词 SS-quasinormal subgroup p-nilpotency finite group
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The Nilpotent Probability of Finite Groups 认领 引用
10
作者 Huaquan Wei Xuanyou Hou +3 位作者 Changman Sun Xixi Diao Hui Wu Liying Yang 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2025年第4期1238-1246,共9页
Let G be a finite group.We denote byν(G)the probability that two randomly chosen elements of G generate a nilpotent subgroup.In this paper,we characterize the structure of finite groups G with lower bounds\({1\over p... Let G be a finite group.We denote byν(G)the probability that two randomly chosen elements of G generate a nilpotent subgroup.In this paper,we characterize the structure of finite groups G with lower bounds\({1\over p},\,{{p^{2}+8}\over{9p^{2}}}\)and\({p+3}\over{4p}\)onν(G),where p is a prime divisor of∣G∣. 展开更多
关键词 Finite group nilpotent probability p-closed supersolvable p-nilpotent
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On Finite Solvable Groups G with m(G)-d(G)=1 认领 引用
11
作者 Hailin LIU Liping ZHONG +1 位作者 Shoushuang CHEN Yulong MA 《Journal of Mathematical Research with Applications》 CSCD 2025年第1期33-38,共6页
Let G be a finite group.A generating set X of G is said to be minimal if no proper subset of X generates G.Let d(G)and m(G)denote the smallest size and the largest size of a minimal generating set of G,respectively.In... Let G be a finite group.A generating set X of G is said to be minimal if no proper subset of X generates G.Let d(G)and m(G)denote the smallest size and the largest size of a minimal generating set of G,respectively.In this paper we present a characterization for finite solvable groups G such that m(G)-d(G)=1 and m(G)≥m(G/N)+m(N)for any non-trivial normal subgroup N of G. 展开更多
关键词 finite solvable group minimal generating set normal subgroup cyclic group
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On weakly S-embedded subgroups of finite groups 认领 引用 被引量：3
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作者 LI JinBao CHEN GuiYun CHEN RuiFang 《Science China Mathematics》 SCIE 2011年第9期1899-1908,共10页
Let H be a subgroup of a group G. Then H is said to be S-quasinormal in G if HP = PH for every Sylow subgroup P of G; H is said to be S-quasinormally embedded in G if a Sylow p-subgroup of H is also a Sylow p-subgroup... Let H be a subgroup of a group G. Then H is said to be S-quasinormal in G if HP = PH for every Sylow subgroup P of G; H is said to be S-quasinormally embedded in G if a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G for each prime p dividing the order of H. In this paper, we say that H is weakly S-embedded in G if G has a normal subgroup T such that HT is an S-quasinormal subgroup of G and H VIT ≤ HSE, where HSE denotes the subgroup of H generated by all those subgroups of H which are S-quasinormally embedded in G. Some results about the influence of weakly S-embedded subgroups on the structure of finite groups are given. 展开更多
关键词 finite groups weakly S-embedded subgroups the generalized Fitting subgroups supersolublegroups p-nilpotent groups
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Criteria of Existence of Hall Subgroups in Non-soluble Finite Groups 认领 引用 被引量：1
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作者 Wen Bin GUO A. N. SKIBA 《Acta Mathematica Sinica,English Series》 SCIE 2010年第2期295-304,共10页
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
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Finite Groups with Seminormal Sylow Subgroups 认领 引用 被引量：1
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作者 Wen Bin GUO 《Acta Mathematica Sinica,English Series》 SCIE 2008年第10期1751-1757,共7页
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 gro... 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. 展开更多
关键词 finite groups seminormal subgroups Sylow subgroups p-soluble groups p-supersoluble groups
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The influence of X-semipermutability of subgroups on the structure of finite groups 认领 引用 被引量：1
15
作者 CHEN GuiYun LI JinBao 《Science China Mathematics》 2009年第2期261-271,共11页
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 ... 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. 展开更多
关键词 finite groups X-semipermutable subgroups supersoluble groups p-nilpotent groups subnormal subgroups Sylow subgroups cyclic subgroups 20D10 20D15 20D20 20D25 20D35
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Symmetric Cayley graphs or bi-Cayley graphs of nite simple groups and valency ten 认领 引用
16
作者 LI Jingjian LI Wen 《纯粹数学与应用数学》 2026年第2期292-307,共16页
A graphΓis a Cayley graph on G if and only if AutΓhas a subgroup G acting regularly on VΓ,and a bipartite graphΓis a bi-Cayley graph on a group G if G≤AutΓacts faithfully and regularly on each part ofΓ.In this ... A graphΓis a Cayley graph on G if and only if AutΓhas a subgroup G acting regularly on VΓ,and a bipartite graphΓis a bi-Cayley graph on a group G if G≤AutΓacts faithfully and regularly on each part ofΓ.In this paper,a complete classification is given for the symmetric Cayley graphs or bi-Cayley graphs on a finite simple group of valency ten which admit quasiprimitive or bi-quasiprimitive groups,respectively. 展开更多
关键词 Cayley graph bi-Cayley graph symmetric finite simple group
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On Distance Laplacian Spectra of Certain Finite Groups 认领 引用
17
作者 Bilal Ahmad RATHER Shariefuddin PIRZADA Guo Fei ZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第4期603-617,共15页
For a finite group G,the power graph P(G)is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x and y are adjacent if and only if xi=y or yi=x,for 2≤i,j≤n.In this ... For a finite group G,the power graph P(G)is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x and y are adjacent if and only if xi=y or yi=x,for 2≤i,j≤n.In this paper,we obtain the distance Laplacian spectrum of power graphs of finite groups such as cyclic groups,dihedral groups,dicyclic groups,abelian groups and elementary abelian p groups.Moreover,we find the largest and second smallest distance Laplacian eigenvalue of power graphs of such groups. 展开更多
关键词 Laplacian matrix distance Laplacian matrix finite groups power graphs
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On Existence of Hall Subgroups in Finite Groups 认领 引用
18
作者 Yufeng Liu Wenbin Guo N. Skiba 《Algebra Colloquium》 SCIE CSCD 2017年第1期75-82,共8页
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
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A question on partial CAP-subgroups of finite groups 认领 引用
19
作者 BALLESTER-BOLINCHES Adolfo ESTEBAN-ROMERO Ramón LI YangMing 《Science China Mathematics》 SCIE 2012年第5期961-966,共6页
A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series.The structural impact of the partial cover and avoid... A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series.The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors.However,there are still some open questions which deserve an answer.The purpose of the present paper is to give a complete answer to one of these questions. 展开更多
关键词 finite groups minimal subgroups partial cover and avoidance property saturated formations
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Special Blocks of Finite Groups 认领 引用
20
作者 Ji Ping ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第1期115-123,共9页
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 eithe... 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. 展开更多
关键词 Finite groups representations blocks defect groups
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