Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal sub...Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G.Some previously known results are generalized.展开更多
This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hype...This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.展开更多
A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are...A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.展开更多
In this paper, we obtain some classification theorems of finite simple groups with two subgroups of coprime indices which are both supersolvable or one supersolvable and the other nilpotent. Using these classification...In this paper, we obtain some classification theorems of finite simple groups with two subgroups of coprime indices which are both supersolvable or one supersolvable and the other nilpotent. Using these classification theorems, we prove some sufficient conditions of finite solvable groups. Finally, we provide a supplement of Doerks Theorem.展开更多
Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = ...Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.展开更多
A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure ...A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 < |D| < |P| such that every subgroup of P with order |D| or 2|D| whenever p = 2 and |D| = 2 is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.展开更多
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal sub...Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called c^＊-quasinormally embedded in G if there is a subgroup T of G such that G = HT and HCqT is s-quasinormally embedded in G. We investigate the influence of c^＊-quasinormally embedded subgroups on the structure of finite groups. Some recent results are generalized.展开更多
In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.
基金The author is supported in part by NSF of China and NSF of Guangdong Province
文摘Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G.Some previously known results are generalized.
基金Research of the first author is supported by a NNSF grant of China(Grant No.11371335)Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Science.The second author was supported by the Russian Foundation for Basic Research(Project No.13-01-00469)+1 种基金the Complex Program of UB RAS(Project 15-16-1-5)under the Agreement 02.A03.21.0006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and Ural Federal University.
文摘In this paper,we determine the finite minimal non-supersolvable groups decomposable into the product of two normal supersolvable subgroups.
文摘This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.
基金the National Natural Science Foundation of China(10471085)the Shanghai Pujiang Program(05PJ14046)the Special Funds for Major Specialities of Shanghai Education Committee
文摘A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.
文摘In this paper, we obtain some classification theorems of finite simple groups with two subgroups of coprime indices which are both supersolvable or one supersolvable and the other nilpotent. Using these classification theorems, we prove some sufficient conditions of finite solvable groups. Finally, we provide a supplement of Doerks Theorem.
基金supported by the Deanship of Scientific Research(DSR) at King Abdulaziz University(KAU) represented by the Unit of Research Groups through the grant number(MG/31/01) for the group entitled "Abstract Algebra and its Applications"
文摘Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.
基金supported by National Natural Science Foundation of China (Grant No. 10771132)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200802800011)+1 种基金the Research Grant of Shanghai University, Shanghai Leading Academic Discipline Project (Grant No. J50101)Natural Science Foundation of Anhui Province (Grant No.KJ2008A030)
文摘A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 < |D| < |P| such that every subgroup of P with order |D| or 2|D| whenever p = 2 and |D| = 2 is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11071229） and the Natural Science Foundation the Jiangsu Higher Education Institutions （Grant No. J0KJD110004）.
文摘Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called c^＊-quasinormally embedded in G if there is a subgroup T of G such that G = HT and HCqT is s-quasinormally embedded in G. We investigate the influence of c^＊-quasinormally embedded subgroups on the structure of finite groups. Some recent results are generalized.
基金This work was supported by the National Natural Science Foundation of China,the Natural Science Foundation of Guangdong ProvinceFund from Education Ministry of China and ARC of ZSU.
文摘In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.
