A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditional...A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.展开更多
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.
A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, som...A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting results are generalized.展开更多
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 a = {σi｜ i ∈ I} be some partition of the set of all primes P, G a finite group and σ（G） = {σi｜σi ∩ π （G） ≠ Ф}. A set H of subgroups of G is said to be a complete Hall or-set of G if every member ≠...Let a = {σi｜ i ∈ I} be some partition of the set of all primes P, G a finite group and σ（G） = {σi｜σi ∩ π （G） ≠ Ф}. A set H of subgroups of G is said to be a complete Hall or-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some σi ∈ σ and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ（G）. A subgroup H of G is said to be： σ-semipermutablc in G with respect to H if HHi x = Hi x H for all x ∈ G and all x ∈ G and all Hi ∈H such that （｜H｜, ｜Hi｜） = 1; σ-semipermutable in G if H is σ-semipermutable in G with respect to some complete Hall σ-set of G. We study the structure of G being based on the assumption that some subgroups of G are σ-semipermutable in G.展开更多
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.
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
基金The Scientific Research Foundation of Sichuan Provincial Education Department of China(No.08zb082)
文摘A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.
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. 10771180)Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 08zb059)Research Programme of Chengdu University of Information Technology
文摘A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting 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 NNSF(Grant No.11771409)Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences
文摘Let a = {σi｜ i ∈ I} be some partition of the set of all primes P, G a finite group and σ（G） = {σi｜σi ∩ π （G） ≠ Ф}. A set H of subgroups of G is said to be a complete Hall or-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some σi ∈ σ and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ（G）. A subgroup H of G is said to be： σ-semipermutablc in G with respect to H if HHi x = Hi x H for all x ∈ G and all x ∈ G and all Hi ∈H such that （｜H｜, ｜Hi｜） = 1; σ-semipermutable in G if H is σ-semipermutable in G with respect to some complete Hall σ-set of G. We study the structure of G being based on the assumption that some subgroups of G are σ-semipermutable in G.
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 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.
