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1.
A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F(G), where Z∞F(G) is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.  相似文献   

2.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S4-free and every minimal subgroup of P n GN is c-supplemented in NG(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized.  相似文献   

3.
A subgroup H of a finite group G is called a c*-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an S-quasinormal embedded subgroup of G. In this paper, the structure of a finite group G with some c*-normal maximal subgroups of Sylow subgroups is characterized and some known related results are generalized.  相似文献   

4.
In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = ...  相似文献   

5.
Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding property of subgroups to characterize the p-supersolvability of finite groups,and obtain some interesting results which improve some recent results.  相似文献   

6.
Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in Φ(G) have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified.  相似文献   

7.
Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown: (1) G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; (2) G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F(H), the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.  相似文献   

8.
Let G be a finite group.A subgroup H of G is called an H-subgroup in G if NG(H) ∩Hg≤H for all g∈G.A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G=HK and H∩K is an H-subgroup in G.In this paper,we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G.Our results improve and generalize several recent results in the literature.  相似文献   

9.
关于有限群的$CAP$-嵌入子群   总被引:1,自引:0,他引:1       下载免费PDF全文
A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H, there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the CAP-embedded property in the group.  相似文献   

10.
In this paper, we give some sufficient conditions for products of two supersolvable sub-groups to be supersolvable groups. Our results generalize some known results.Theorem 1 Let G = HK,(|H|,|K|) = 1, Where H and K are two supersolvable sub-groups. If H is commutative with every maximal subgroup of K, and K is commutative with every maximal subgroup of H, then G is supersolvable.Theorem 2 Let G = HK, H ∩ K = 1, H G, and K be quasinormal in H. If H, K are supersolvable, the G is supersolvable.Theorem 3 Let G= HK,(|H|,|K|) = 1,H,K be two supersolvable subgroups. If H is commutative with any Sylow subgroup of K and any maximal subgroup of every sylow subgroup of K, and K is commutative with any sylow subgroup of H and any maximal subgroup of every sylow subgroup of H, then G is supersolvable. Theorem 4 If H,K are two supersolvable subgroups of G, G= HK, G′is nilpotent, H is quasi normal K, and K is quasi normal in H,then G is supersolvable. Theorem 5 If H,K are two supersolvable subgroups of G, G= HK, H′? G,[H,K]? G,[H,K] is nilpotent, H is quasi normal in K, and K is quasi normal in H,then G is supersolvable.  相似文献   

11.
12.
In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G p |<∞ (of course, it contains G = G p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.  相似文献   

13.
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.  相似文献   

14.
For any integer n ≠ 0,1, a group G is said to be “n-Bell” if it satisfies the identity [x n ,y] = [x,y n ]. It is known that if G is an n-Bell group, then the factor group G/Z 2(G) has finite exponent dividing 12n 5(n ? 1)5. In this article we show that this bound can be improved. Moreover, we prove that every n-Bell group is n-nilpotent; consequently, using results of Baer on finite n-nilpotent groups, we give the structure of locally finite n-Bell groups. Finally, we are concerned with locally graded n-Bell groups for special values of n.  相似文献   

15.
Bijan Taeri 《代数通讯》2013,41(3):894-922
Let n be an integer greater than 1. A group G is said to be n-rewritable whenever for every n elements x 1,…,x n of G, there exist distinct permutations τ, σ on the set {1,2,…, n} such that x τ(1) ··· x τ(n) = x σ (1) ··· x σ (n). In this article, we complete the classification of 3-rewritable finite nilpotent groups and prove that a finite nilpotent group G is 3-rewritable if and only if G has an abelian subgroup of index 2 or the derived subgroup has order < 6.  相似文献   

16.
17.
《代数通讯》2013,41(5):1417-1425
ABSTRACT

Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Qn-group) if for every n elements x1, x2,…,xn in G there exist distinct permutations σ and τ in Sn such that xσ(1)xσ (2) ??? xσ(n) = xτ(1)xτ(2) ??? xτ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law.  相似文献   

18.
In this paper we prove that if R is a commutative Noetherian local pro-p domain of characteristic 0, then every finitely generated R-standard group is linear. This work has been partially supported by the FEDER, the MEC Grant MTM2004-04665 and the Ramón y Cajal Program.  相似文献   

19.
A Garside group is a group admitting a finite lattice generating set . Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice , and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(π, 1)s enjoy Bestvina's weak nonpositive curvature condition. Under a certain tameness condition, this implies that every solvable subgroup of G is virtually Abelian.  相似文献   

20.
All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.  相似文献   

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