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Local Characterizations of Results on the Normal Index of Subgroups in Finite Groups 认领 引用
1
作者 Yubo LV Yangming LI Xiaoxia DONG 《Journal of Mathematical Research with Applications》 CSCD 2026年第1期33-39,共7页
Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/HG,where K is a normal supplement of H in G such that|K|is minimal and HG≤K■G.Let p be a prime which divide... Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/HG,where K is a normal supplement of H in G such that|K|is minimal and HG≤K■G.Let p be a prime which divides the order of a group G.In this paper,some characterizations of G being p-solvable or p-supersolvable were obtained by analyzing the normal index of certain subgroups of G.These results can be viewed as local version of recent results in the literature. 展开更多
关键词 p-solvable group p-supersolvable group normal index maximal subgroup 2-maximal subgroup
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LOCAL SS-QUASINORMALITY OF SOME SUBGROUPS OF FINITE GROUPS 认领 引用
2
作者 WEI Hua-quan WU Hui HE Jia-wen 《数学杂志》 2026年第2期63-74,共12页
This paper investigates the in uence of local SS-quasinormal maximal subgroups of Sylow subgroups on the structure of nite groups.We present several new criteria on p-nilpotency of nite groups by utilizing a small qua... This paper investigates the in uence of local SS-quasinormal maximal subgroups of Sylow subgroups on the structure of nite groups.We present several new criteria on p-nilpotency of nite groups by utilizing a small quantity of local SS-quasinormal maximal subgroups of Sylow p-subgroups.As applications,we obtain some sucient conditions for a nite group to be in a saturated formation containing the class of supersolvable groups. 展开更多
关键词 nite group maximal subgroup p-nilpotent group SS-quasinormal group
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TI-subgroups and P-subnormal subgroups and the structure of nite groups 认领 引用
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作者 CHEN Ruifang ZHAO Xianhe 《纯粹数学与应用数学》 2026年第1期33-45,共13页
Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩Hg=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K0≤K1≤K2≤…≤Kn-1≤Kn=G suc... Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩Hg=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K0≤K1≤K2≤…≤Kn-1≤Kn=G such that|Ki:Ki-1|∈P for i∈{1;2;…;n}.Furthermore,K is called K-P-subnormal in G if there is a chain of subgroups K=K0≤K1≤K2≤…≤Kn-1≤Kn=G such that either Ki-1is normal in Ki or|Ki:Ki-1|∈P for i∈{1;2;…;n}.In this paper,some properties of a nite group in which some particular subgroups are TI-subgroups or P-subnormal subgroups or K-P-subnormal subgroups are given. 展开更多
关键词 TI-subgroup P-subnormal subgroup K-P-subnormal subgroup soluble group
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The Influence of Second Maximal Subgroups on the Structure of Group Class Jpr 认领 引用
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作者 Lin YANG Wei LIU +1 位作者 Shuqin DONG Hongwei BAO 《Journal of Mathematical Research with Applications》 CSCD 2025年第5期629-636,共8页
In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class Jpris presented by establishing the r... In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class Jpris presented by establishing the relationship between the core and the second maximal subgroups in these classifications. 展开更多
关键词 maximal subgroups second maximal subgroups group class Jpr
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On θ*-completions of F-abnormal Subgroups 认领 引用
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作者 高辉 高胜哲 尹丽 《Chinese Quarterly Journal of Mathematics》 2016年第4期406-411,共6页
Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we inve... Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*-completions of F-abnormal subgroups. 展开更多
关键词 θ*-completions maximal subgroups 2-maximal subgroups F-abnormal subgroups
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Some Generalized Normal Subgroups and p-nilpotency of Finite Groups 认领 引用 被引量：1
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作者 ZHONG Guo LIN Shi-Xun +1 位作者 CHEN Qi-le QIN Li-hua 《Chinese Quarterly Journal of Mathematics》 2018年第1期17-24,共8页
In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
关键词 s-semipermutable subgroups c#-normal subgroups subnormally embedded subgroups ss-quasinormal subgroups p-nilpotency
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On σ-c-propermutable Subgroups of Finite Groups 认领 引用
7
作者 MA Xiaojian MAO Yuemei 《数学进展》 CSCD 北大核心 2025年第3期509-517,共9页
Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=NG(H)B and for every Hall σi-subgroup Bi of B,there exists an element x∈B such that HBi^(... Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=NG(H)B and for every Hall σi-subgroup Bi of B,there exists an element x∈B such that HBix=Bix H.In this paper,the influence of σ-c-propermutable subgroups on the structure of finite groups is investigated,and some criteria for a normal subgroup of G to be hypercyclically embedded in G are derived. 展开更多
关键词 complete Hallσ-set σ-c-propermutable subgroup supersoluble group hypercyclically embedded
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ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS 认领 引用 被引量：9
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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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On s*-Completions of Maximal Subgroups of Finite Groups 认领 引用 被引量：1
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作者 高辉 高胜哲 尹丽 《Chinese Quarterly Journal of Mathematics》 2015年第3期381-388,共8页
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... 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 subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable. 展开更多
关键词 maximal subgroups θ＊-completions s＊-completions solvable groups super-solvable groups
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Fully Secure Identity-based Broadcast Encryption in the Subgroups 认领 引用 被引量：4
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作者 张乐友 胡予濮 吴青 《China Communications》 SCIE CSCD 2011年第2期152-158,共7页
In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive se... In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security. 展开更多
关键词 identity-based broadcast encryption dual system encryption full security static assumption subgroup provable security
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On Φ-τ-Supplement Subgroups of Finite Groups 认领 引用 被引量：1
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作者 Xiaojian MA Yuemei MAO 《Journal of Mathematical Research with Applications》 CSCD 2017年第3期281-289,共9页
Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/H_G and H= H/H_G. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T... Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/H_G and H= H/H_G. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T and H∩T≤SΦ（H）. In this paper,some new characterizations of hypercyclically embedability and p-nilpotency of a finite group are obtained based on the assumption that some primary subgroups are Φ-τ-supplement in G. 展开更多
关键词 Sylow subgroups subnormal subgroups subgroup functor p-nilpotent group Φ-τ-supplement
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Finite Groups with Some Cp-Supplemented Subgroups 认领 引用 被引量：1
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作者 Yubo LV Yangming LI 《Journal of Mathematical Research with Applications》 CSCD 2023年第1期74-82,共9页
Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis t... Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis the core of H in G.A CSp-group is a group in which every p-subgroup is cp-supplemented.In this paper,we characterize the p-solvability and psupersolvability of groups G with some certain p-subgroups being cp-supplemented.Furthermore,we give some equivalent conditions of CSp-group in p-solvable universe.Finally,we give some criteria of CSp-groups for the direct product of two CSp-groups.Our results extend some recent conclusions. 展开更多
关键词 c-supplemented subgroup Cp-normal subgroup Cp-supplemented subgroup CSpgroup p-supersolvable group
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On the Equal-height Elements of the Fuzzy Subgroups 认领 引用 被引量：3
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作者 张诚一 胡丽萍 党平安 《Chinese Quarterly Journal of Mathematics》 2001年第2期82-85,共4页
The properties of the equal height elements of the fuzzy subroups and the classification of groups by its fuzzy subgroups are discussed.
关键词 group fuzzy subgroup equivalence equal height element
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Finite Groups with Some Subgroups Weakly s-Permutably Embedded 认领 引用
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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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The Lattice of Fully Invariant Subgroups of the Cotorsion Hull 认领 引用 被引量：1
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作者 Tariel Kemoklidze 《Advances in Pure Mathematics》 2013年第8期670-679,共10页
The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case ... The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice. 展开更多
关键词 Lattice of Fully Invariant Subgroups Direct Sum of Torsion-Complete Groups Cotorsion Hull
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Carter subgroups of singular classical groups over finite fields 认领 引用
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作者 高有 石新华 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2004年第3期341-346,共6页
Let F q be a finite field with qelements where q=p~α. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (n+t,n)(F q), singular unitary group U (n+... Let F q be a finite field with qelements where q=p~α. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (n+t,n)(F q), singular unitary group U (n+t,n)(F (q^2)) and singular orthogonal group O (n+t,n)(F q)(n is even) over finite fields F q. 展开更多
关键词 finite field singular classical groups Carter subgroup
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Finite Groups with Only s-quasinormal and Abnormal Subgroups 认领 引用 被引量：2
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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 Whose Norm Quotient Groups Have Cyclic Sylow Subgroups 认领 引用
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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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EFFECTS OF MEDICINAL MOXIBUSTION ON SERUM GASTRIN,URINARY D-XYLOSE EXCRETORY RATE AND T CELL SUBGROUPS IN SPLEEN DEFICIENCY PATIENTS 认领 引用
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作者 周建伟 张凡 肖鸣 《World Journal of Acupuncture-Moxibustion》 CAS 1997年第2期18-21,共4页
The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as cont... The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as control were treated by pure moxa stick. After treatment, the serum gastrin, urinary D - xylose excretory rate and T cell subgroups in patients with spleen deficiency have been greatly improved as compared with those before treatment in two groups (P< 0.01 or 0.05). Comparing the changes of the indexes between treatment group and control group, there were significant(P<0.05), or markedly significant(P<0.01) differences. It indicated that the medicinal moxibustion could improve the secreting and absorbing functions of digestive tract and the cellular immune function in patients with spleen deficiency. 展开更多
关键词 Syndrome of spleen deficiency Medicinal moxibustion Serum gastrin Urinary Dxylose excretory rate T cell subgroups
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Subgroups of chronic fatigue syndrome based on psychiatric disorder onset and current psychiatric status 认领 引用
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作者 Molly M. Brown Carly Kaplan +1 位作者 Leonard A. Jason Christopher B. Keys 《Health》 2010年第2期90-96,共7页
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 impairmen... 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. 展开更多
关键词 Chronic Fatigue Syndrome Psychiatric Comorbidity Subgroups Impairment
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