共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhangjia Han 《Proceedings Mathematical Sciences》2010,120(2):141-148
A subgroup H of a group is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. Using the concept of s-semipermutable subgroups, some new characterizations of p-nilpotent groups are obtained and several results are generalized. 相似文献
2.
Let G be a finite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permutes with all Sylow subgroups Q of G such that (|Q|, |H|) = 1 and (|H|, |Q
G
|) ≠ 1; (2) H is weakly τ-quasinormal in G if G has a subnormal subgroup T such that HT = G and T ∩ H ≦ H
τG
, where H
τG
is the subgroup generated by all those subgroups of H which are τ-quasinormal in G. Our main result here is the following. Let ℱ be a saturated formation containing all supersoluble groups and let X ≦ E be normal subgroups of a group G such that G/E ∈ ℱ. Suppose that every non-cyclic Sylow subgroup P of X has a subgroup D such that 1 < |D| < |P| and every subgroup H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is non-Abelian) not having a supersoluble supplement in G is weakly τ-quasinormal in G. If X is either E or F* (E), then G ∈ ℱ. 相似文献
3.
Na Tang Wenbin Guo V. V. Kabanov 《Proceedings of the Steklov Institute of Mathematics》2007,257(1):S189-S194
A subgroup H of a group G is called s-semipermutable in G if H is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, we use s-semipermutable subgroups to determine the structure of finite groups. Some of the previous results are generalized. 相似文献
4.
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 H??T 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. 相似文献
5.
M. Asaad 《Acta Mathematica Hungarica》2014,144(2):499-514
Let G be a finite group and H a subgroup of G. We say that H is s-permutable in G if HP = PH for all Sylow subgroups P of G; H is s-semipermutable in G if HP = PH for all Sylow subgroups P of G with (|P|, |H|) = 1. Let H s G be the subgroup of H generated by all those subgroups of G which are s-permutable in G and H sG the intersection of all such s-permutable subgroups of G contain H. We say that H is nearly s-embedded in G if G has an s-permutable subgroup T such that H sG = HT and \({H \cap T \leqq H_{ssG}}\) , where H ssG is an s-semipermutable subgroup of G contained in H. In this paper, we study the structure of a finite group G under the assumption that some subgroups of prime power order are nearly s-embedded in G. A series of known results are improved and extended. 相似文献
6.
Yangming Li 《代数通讯》2013,41(11):4202-4211
Suppose that G is a finite group and H is a subgroup of G. H is said to be S-quasinormal in G if it permutes with every Sylow 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. We investigate the influence of S-quasinormally embedded subgroups on the structure of finite groups. Some recent results are generalized. 相似文献
7.
Manuel J. Alejandre A. Ballester-Bolinches M. C. Pedraza-Aguilera 《Journal of Algebra》2001,240(2):207
A finite group G is said to be a PST-group if every subnormal subgroup of G permutes with every Sylow subgroup of G. We shall discuss the normal structure of soluble PST-groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaining information about the global property. Moreover, a new approach to soluble PT-groups, i.e., soluble groups in which permutability is a transitive relation, follows naturally from our vision of PST-groups. Our techniques and results provide a unified point of view for T-groups, PT-groups, and PST-groups in the soluble universe, showing that the difference between these classes is quite simply their Sylow structure. 相似文献
8.
Suppose that G is a finite group and H is a subgroup of G. H is said to be weakly s-semipermutable in G if there are a subnormal subgroup T of G and an s-semipermutable subgroup \(H_{ssG}\) of G contained in H such that \(G=HT\) and \(H\cap T\le H_{ssG}\); H 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. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying \(1<|D|<|P|\) and study the structure of G under the assumption that every subgroup H of P with \(|H|=|D|\) is either weakly s-semipermutable or ss-quasinormal in G. Some recent results are generalized and unified.
相似文献9.
It is proved that if G is a split extension of a cyclic p-group by a cyclic p′-group with faithful action then any torsion unit of augmentation one of G is rationally conjugate to a group element. It is also proved that if G is a split extension of an abelian group A by an abelian group X with (|A|, |X|) = 1 then any torsion unit of G of augmentation one and order relatively prime to |A| is rationally conjugate to an element of X. 相似文献
10.
Let G be a finite group. Goldschmidt, Flores, and Foote investigated the concept: Let K ≤ G. A subgroup H of K is called strongly closed in K with respect to G if H g ∩ K ≤ H for all g ∈ G. In particular, when H is a subgroup of prime-power order and K is a Sylow subgroup containing it, H is simply said to be a strongly closed subgroup. Bianchi and the others called a subgroup H of G an H-subgroup if N G (H) ∩ H g ≤ H for all g ∈ G. In fact, an H-subgroup of prime power order is the same as a strongly closed subgroup. We give the characterizations of finite non-T-groups whose maximal subgroups of even order are solvable T-groups by H-subgroups or strongly closed subgroups. Moreover, the structure of finite non-T-groups whose maximal subgroups of even order are solvable T-groups may be difficult to give if we do not use normality. 相似文献
11.
Suppose G is a finite group and H is 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 H se of G contained in H such that G = HT and H ∩ T ≤ H se . We investigate the influence of weakly s-permutably embedded subgroups on the structure of finite groups. Some recent results are generalized. 相似文献
12.
Qingjun Kong 《Acta Mathematica Hungarica》2014,142(2):459-467
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 the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G; H 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. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying 1<|D|<|P| and study the structure of G under the assumption that every subgroup H of P with |H|=|D| is either S-quasinormally embedded or SS-quasinormal in G. Some recent results are generalized and unified. 相似文献
13.
A subgroup H of a group G is said to be an SS-quasinormal (Supplement-Sylow-quasinormal) subgroup if there is a subgroup B of G such that HB = G and H permutes with every Sylow subgroup of B. A subgroup H of a group G is said to be S-quasinormally embedded inGif for every Sylow subgroup P of H, there is an S-quasinormal subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain SS-quasinormal or S-quasinormally embedded subgroups of prime power order are studied. 相似文献
14.
Qinhai Zhang 《代数通讯》2013,41(9):4515-4524
A subgroup H of a group G is called s-semipermutable in G if it is permutable with all Sylow p-subgroups of G with (p,∣H∣) for all primes p such that p ∥G ∣. In this pa-per, we investigate the influence of s-semipermutable and abnormal subgroups on the structure of a finite group and classify such finite groups in which every subgroup is either s-semipermutable or abnormal. 相似文献
16.
We prove that a transitive permutation group of degree n with a cyclic point stabilizer and whose order is n(n-1) is isomorphic to the affine group of degree 1 over a field with n elements. More generally we show that if a finite group G has an abelian and core-free Hall subgroup Q, then either Q has a small order (2|Q|2 < |G|) or G is a direct product of 2-transitive Frobenius groups. 相似文献
17.
We study products of Sylow subgroups of a finite group G. First we prove that G is solvable if and only if G = P1 ... Pm for any choice of Sylow pi-subgroups Pi , where p1,..., pm are all of the distinct prime divisors of |G|, and for any ordering of the pi . Then, for a general finite group G, we show that the intersection of all Sylow products as above is a subgroup of G which is closely related to the solvable radical of G.
Received: 18 November 2004 相似文献
18.
A subgroup H of a finite group G is said to be SS-permutable in G if H has a supplement K in G such that H permutes with every Sylow subgroup of K. A finite group G is called an SST-group if SS-permutability is a transitive relation on the set of all subgroups of G. The structure of SST-groups is investigated in this paper. 相似文献
19.
A subgroup of a group G is said to be Sylow-quasinormal (S-quasinormal) in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be Supplement-Sylow-quasinormal (SS-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this article, we investigate the influence of SS-quasinormal of maximal or minimal subgroups of Sylow subgroups of the generalized Fitting subgroup of a finite group. 相似文献
20.
Khaled A. Al-Sharo 《代数通讯》2013,41(1):315-326
We say that a subgroup H of a finite group G is nearly S-permutable in G if for every prime p such that (p, |H|) = 1 and for every subgroup K of G containing H the normalizer N K (H) contains some Sylow p-subgroup of K. We study the structure of G under the assumption that some subgroups of G are nearly S-permutable in G. 相似文献