共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Jiakuan Lu 《代数通讯》2013,41(10):3726-3732
A subgroup H of a finite group G is called a QTI-subgroup if C G (x) ≤ N G (H) for any 1 ≠ x ∈ H. In this article, the finite groups all of whose second maximal subgroup are QTI-subgroups are classified. 相似文献
3.
Long Miao 《Bulletin of the Brazilian Mathematical Society》2010,41(2):223-235
A subgroup H of a group G is said to be weakly s-permutable in G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K ≤ H
sG
where H
sG
is the largest s-quasinormal subgroup of G contained in H. In this paper, we investigate the influence of weak s-permutability of some primary subgroups in finite groups. Some new results about p-supersolvability and p-nilpotency of finite groups are obtained. 相似文献
4.
《代数通讯》2013,41(10):4807-4816
Abstract A subgroup H of G is said to be c-normal in G if there exists a normal subgroup N of G such that HN = G and H ∩ N ≤ H G = Core(H). We extend the study on the structure of a finite group under the assumption that all maximal or minimal subgroups of the Sylow subgroups of the generalized Fitting subgroup of some normal subgroup of G are c-normal in G. The main theorems we proved in this paper are: Theorem Let ? be a saturated formation containing 𝒰. Suppose that G is a group with a normal subgroup H such that G/H ∈ ?. If all maximal subgroups of any Sylow subgroup of F*(H) are c-normal in G, then G ∈ ?. Theorem Let ? be a saturated formation containing 𝒰. Suppose that G is a group with a normal subgroup H such that G/H ∈ ?. If all minimal subgroups and all cyclic subgroups of F*(H) are c-normal in G, then G ∈ ?. 相似文献
5.
A subgroup H of G is said to be S-embedded in G if G has a normal subgroup N such that HN is s-permutable in G and H ∩ N ⩽ H
sG
, where H
sG
is the largest s-permutable subgroup of G contained in H. S-embedded subgroups are used to give novel characterizations for some classes of groups. New results are obtained and a number
of previously known ones are generalized. 相似文献
6.
Let G be a finite group. A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H G , where H G = Core G (H) is the largest normal subgroup of G contained in H. In this article, we investigate the structure of a finite group G under the assumption that subgroups of prime order are c-supplemented in G. Moreover, we analyze the structure of a group G when the minimal subgroups of the generalized Fitting subgroup F?(G) of G are c-supplemented in G through the theory of formations. 相似文献
7.
Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N G (K) ∩ K x ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P 0 ? P 1 ? ··· ? P n = P is called a maximal chain of P provided that |P i : P i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P 0 ? P 1 ? ··· ? P i ? ··· ? P n = P such that P i ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups. 相似文献
8.
Shouhong Qiao 《印度理论与应用数学杂志》2013,44(6):795-808
A subgroup H of a group G is said to be weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ H sG , where H sG is the maximal s-permutable subgroup of G contained in H. In this paper, we investigate the influence of weakly s-supplemented subgroups on the structure of finite groups. Some recent results are generalized. 相似文献
9.
A subgroup H is called ?-supplemented in a finite group G, if there exists a subgroup B of G such that G = HB and H 1 B is a proper subgroup of G for any maximal subgroup H 1 of H. In this article, we investigate the influence of ?-supplementation of some primary subgroups in finite groups. Some new results about supersolvable groups and formation are obtained. 相似文献
10.
Mohamed Asaad 《代数通讯》2013,41(6):2319-2330
Let G be a finite group. A subgroup H of G is said to be weakly s-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ H s G , where H s G is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G. In this article, we investigate the structure of G under the assumption that some families of subgroups of G are weakly s-supplemented in G. Some recent results are generalized. 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.
Let H be a subgroup of a finite group G. H is said to be λ-supplemented in G if G has a subgroup T such that G = HT and H ∩ T ≤ H SE , where H SE denotes the subgroup of H generated by all those subgroups of H, which are S-quasinormally embedded in G. In this article, some results about the λ-supplemented subgroups are obtained, by which we determine the structure of some classes of finite groups. In particular, some new characterizations of p-supersolubility of finite groups are given under the assumption that some primary subgroups are λ-supplemented. As applications, a number of previous known results are generalized. 相似文献
13.
Yanming Wang 《Journal of Algebra》1996,180(3):954
A subgroupHis calledc-normal in groupGif there exists a normal subgroupNofGsuch thatHN=GandH∩N≤HG, where[formula]is the maximal normal subgroup ofGwhich is contained inH. We obtain some results about thec-normal subgroups and use them to determine the structures of some groups. 相似文献
14.
J. Cimprič 《代数通讯》2013,41(1):103-119
A subgroup H is called Q-supplemented in a finite group G, if there exists a subgroup K of G such that G = HK and H ∩ K is contained in H QG , where H QG is the maximal quasinormal subgroup of G contained in H. In this article, we investigate the influence of Q-supplementation of some primary subgroups in finite groups. Some recent results are generalized. 相似文献
15.
Constantinos E. Kofinas 《代数通讯》2013,41(4):1575-1593
Let L be a relatively free nilpotent Lie algebra over ? of rank n and class c, with n ≥ 2; freely generated by a set 𝒵. Give L the structure of a group, denoted by R, by means of the Baker–Campbell–Hausdorff formula. Let G be the subgroup of R generated by the set 𝒵 and N Aut(L)(G) the normalizer in Aut(L) of the set G. We prove that the automorphism group of L is generated by GL n (?) and N Aut(L)(G). Let H be a subgroup of finite index in Aut(G) generated by the tame automorphisms and a finite subset X of IA-automorphisms with cardinal s. We construct a set Y consisting of s + 1 IA-automorphisms of L such that Aut(L) is generated by GL n (?) and Y. We apply this particular method to construct generating sets for the automorphism groups of certain relatively free nilpotent Lie algebras. 相似文献
16.
Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H of P with |H| = |D| are c-normal in G. 相似文献
17.
《代数通讯》2013,41(3):1253-1270
Abstract Let G a simple group of type 2 B 2(q) or 2 G 2(q), where q is an odd power of 2 or 3, respectively. The main goal of this paper is to determine the multiplicity free permutation representations of G and A ≤ Aut(G) where A is a subgroup containing a copy of G. Let B be a Borel subgroup of G. If G = 2 B 2(q) we show that there is only one non-trivial multiplicity free permutation representation, namely the representation of G associated to the action on G/B. If G = 2 G 2(q) we show that there are exactly two such non-trivial representations, namely the representations of G associated to the action on G/B and the action on G/M, where M = UC with U the maximal unipotent subgroup of B and C the unique subgroup of index 2 in the maximal split torus of B. The multiplicity free permutation representations of A correspond to the actions on A/H where H is isomorphic to a subgroup containing B if G = 2 B 2(q), and containing M if G = 2 G 2(q). The problem of determining the multiplicity free representations of the finite simple groups is important, for example, in the classification of distance-transitive graphs. 相似文献
18.
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
19.
Suppose that V is a finite faithful irreducible G-module where G is a finite solvable group of odd order. We prove if the action is quasi-primitive, then either F(G) is abelian or G has at least 212 regular orbits on V. As an application, we prove that when V is a finite faithful completely reducible G-module for a solvable group G of odd order, then there exists v ∈ V such that C G (v) ? F 2(G) (where F 2(G) is the 2nd ascending Fitting subgroup of G). We also generalize a result of Espuelas and Navarro. Let G be a group of odd order and let H be a Hall π-subgroup of G. Let V be a faithful G-module over a finite field of characteristic 2, then there exists v ∈ V such that C H (v) ? O π(G). 相似文献
20.
Martino Garonzi 《代数通讯》2013,41(2):471-491