We prove that a finite group G is p-supersolvable or p-nilpotent if some sub- groups of G are weakly s-semipermutable in G. Several earlier results are generalized.
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.
Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable su...Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.展开更多
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
Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under ...Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under the assumption that every member in Md(Gp) is S-semipermutable in G for each prime divisor p of |G| and a Sylow p-subgroup Gp of G.展开更多
A subgroup H of a group G is said to be weakly normal in G if Hg ≤ NG（H） implies that g E NG（H）. In this paper, using the condition that the minimal subgroups or subgroups of prime square order of G are weakly no...A subgroup H of a group G is said to be weakly normal in G if Hg ≤ NG（H） implies that g E NG（H）. In this paper, using the condition that the minimal subgroups or subgroups of prime square order of G are weakly normal in G, we get some results about formation.展开更多
Suppose that H is a subgroup of a finite group G.We call H is semipermutable in G if HK=KH iov any subgroup K of G such that(|H|,|K|)=1;H is s-semipermutable in G if HG_(p)=G_(p)H,for any Sylow p-subgroup G_(p)of G su...Suppose that H is a subgroup of a finite group G.We call H is semipermutable in G if HK=KH iov any subgroup K of G such that(|H|,|K|)=1;H is s-semipermutable in G if HG_(p)=G_(p)H,for any Sylow p-subgroup G_(p)of G such that(|H|,p)=1.These two concepts have been received the attention of many scholars in group theory since they were introduced by Professor Zhongmu Chen in 1987.In recent decades,there are a lot of papers published via the application of these concepts.Here we summarize the results in this area and gives some thoughts in the research process.展开更多
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably 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-permutable subgrou...Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably 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-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H n T ≤ Hse. In this paper, we continue the work of [Comm. Algebra, 2009, 37： 1086-1097] to study the influence of the weakly s-permutably embedded subgroups on the structure of finite groups, and we extend some recent results.展开更多
By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and sup...By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.展开更多
基金Research of the authors is supported by NNSF of China （Grants 11171243 and 11001098）, Natural Science Foundation of Jiangsu （Grant BK20140451）, and University Natural Sci- ence Foundation of Jiangsu （Grant 14KJB110002）.
文摘We prove that a finite group G is p-supersolvable or p-nilpotent if some sub- groups of G are weakly s-semipermutable in G. Several earlier results are generalized.
基金Supported by SRFPYED(2017ZDX041)and SRFPYED(2016ZDX151)
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No.10871210)Natural Science Foundation of Guangdong Province (Grant No.06023728)
文摘Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.
基金supported by National Natural Science Foundation of China (Grant Nos.10771172,11001226)Postgraduate Innovation Foundation of Southwest University (Grant Nos. ky2009013,ky2010007)
文摘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.
基金the National Natural Science Foundation of China (No.10161001)the Natural Science Foundation of Guangxi Autonomous Region (No.0249001)a Research Grant of Shanghai University(No.SHUCX091043)
文摘Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under the assumption that every member in Md(Gp) is S-semipermutable in G for each prime divisor p of |G| and a Sylow p-subgroup Gp of G.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11171243, 11326056） and the Scientific Research Foundation for Doctors, Henan University of Science and Technology （No. 09001610）.
文摘A subgroup H of a group G is said to be weakly normal in G if Hg ≤ NG（H） implies that g E NG（H）. In this paper, using the condition that the minimal subgroups or subgroups of prime square order of G are weakly normal in G, we get some results about formation.
基金supported in part by the project of NSF of China(12071092)the Science and Technology Program of Guangzhou Municipality,China(201804010088).
文摘Suppose that H is a subgroup of a finite group G.We call H is semipermutable in G if HK=KH iov any subgroup K of G such that(|H|,|K|)=1;H is s-semipermutable in G if HG_(p)=G_(p)H,for any Sylow p-subgroup G_(p)of G such that(|H|,p)=1.These two concepts have been received the attention of many scholars in group theory since they were introduced by Professor Zhongmu Chen in 1987.In recent decades,there are a lot of papers published via the application of these concepts.Here we summarize the results in this area and gives some thoughts in the research process.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271085, 11201082）, the Natural Science Foundation of Guangdong Province （S2011010004447）, and the Special Project for the Subject Build of High Education of Guangdong Province （2012KJCX0081）.
文摘Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably 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-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H n T ≤ Hse. In this paper, we continue the work of [Comm. Algebra, 2009, 37： 1086-1097] to study the influence of the weakly s-permutably embedded subgroups on the structure of finite groups, and we extend some recent results.
文摘By using pronormal minimal subgroups and weak left Engel elements ofprime order of the normalizers of Sylow subgroups of a finite group G, we obtain somesufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.
