Let F be a class of finite groups. A subgroup H of a finite group G is said to be Fs-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and （H／cap T）HG/HG is contained in th...Let F be a class of finite groups. A subgroup H of a finite group G is said to be Fs-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and （H／cap T）HG/HG is contained in the F-hypercenter ZF∞ （G/HG） of G/HG. In this paper, we use Fs-quasinormal subgroups to study the structure of finite groups. Some new results are obtained.展开更多
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/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤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/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤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
In this paper, we deal mainly with the following problem: if every 2-maximal subgroup of a Sylow p-subgroup of a finite group G is S-seminormal in G, what conditions force G to be p-nilpotent? As an application of mai...In this paper, we deal mainly with the following problem: if every 2-maximal subgroup of a Sylow p-subgroup of a finite group G is S-seminormal in G, what conditions force G to be p-nilpotent? As an application of main results, some sufficient conditions for finite nilpotent groups and finite supersolvable groups are obtained.展开更多
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
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
Let A be a subgroup of a group G and X a nonempty subset of G. A is called an X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that ...Let A be a subgroup of a group G and X a nonempty subset of G. A is called an X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that AT 1 x = T 1 x A. On the basis of this concept we obtain some new characterizations of finite supersoluble groups.展开更多
Suppose that G is a finite group and H is a subgroup of G.H is said to be a p-CAP-subgroup of G if H either covers or avoids each pd-chief factor of G.We give some characterizations for a group G to be p-solvable unde...Suppose that G is a finite group and H is a subgroup of G.H is said to be a p-CAP-subgroup of G if H either covers or avoids each pd-chief factor of G.We give some characterizations for a group G to be p-solvable under the assumption that some subgroups of G are p-CAP-subgroups of G.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11071147)Doctoral Program Foundation of Institutions of Higher Education of China(Grant No.20113402110036)
文摘Let F be a class of finite groups. A subgroup H of a finite group G is said to be Fs-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and （H／cap T）HG/HG is contained in the F-hypercenter ZF∞ （G/HG） of G/HG. In this paper, we use Fs-quasinormal subgroups to study the structure of finite groups. Some new results are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.12071092)Guangdong Basic and Applied Basic Research Foundation(Grant No.2025A1515012072)+1 种基金the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH051298)the Scientific Research Foundation of Bozhou University(Grant No.BYKQ202419).
文摘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/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤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.
文摘In this paper, we deal mainly with the following problem: if every 2-maximal subgroup of a Sylow p-subgroup of a finite group G is S-seminormal in G, what conditions force G to be p-nilpotent? As an application of main results, some sufficient conditions for finite nilpotent groups and finite supersolvable groups are obtained.
文摘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.
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the National Natural Science Foundation of China (Grant No.10771180) a postgraduate innovation grant of University of Science and Technology of China
文摘Let A be a subgroup of a group G and X a nonempty subset of G. A is called an X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that AT 1 x = T 1 x A. On the basis of this concept we obtain some new characterizations of finite supersoluble groups.
基金supported by the National Natural ScienceFoundation of China(Grant Nos.11871062,12071093)the NSFC-RFBR(Grant No.12011530061)the Natural Science Foundation of Jiangsu Province(Grant No.BK20181451).
文摘Suppose that G is a finite group and H is a subgroup of G.H is said to be a p-CAP-subgroup of G if H either covers or avoids each pd-chief factor of G.We give some characterizations for a group G to be p-solvable under the assumption that some subgroups of G are p-CAP-subgroups of G.
