共查询到20条相似文献,搜索用时 10 毫秒
1.
Xinjian Zhang 《代数通讯》2013,41(10):3652-3657
Let G be a finite group and p a prime. In this article, we give a criterion of p-nilpotency of G by means of the normalizer and a generalization of normality of subgroups. 相似文献
2.
设G是一个有限群,H是G的一个子群.称H为G的一个s-置换子群,若对于G的任意Sylow子群P,成立HP=PH.称H为G的一个弱s-可补的子群.若存在G的一个子群T,使得G=HT且H∩T≤H_s G,其中H_s G是包含在H中的G的最大的s-置换子群.本文在假设G的某些子群是弱s-可补的前提下,得到了G的一个结构定理,并推广了许多近期的结果. 相似文献
3.
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
4.
Khaled A. Al-Sharo 《代数通讯》2013,41(10):3690-3703
Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = PH for all Sylow subgroups P of G; S-permutably embedded in G if each Sylow subgroup of H is also a Sylow subgroup of some S-permutable subgroup of G. Let H be a subgroup of a group G. Then we say that H is SQ-supplemented in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and T ∩ H ≤ C. We study the structure of G under the assumption that some subgroups of G are SQ-supplemented in G. Some known results are generalized. 相似文献
5.
Let G be a finite group written multiplicatively and k a positive integer. If X is a non-empty subset of G, write X
2 = |xy | x, y X . We say that G has the small square property on k-sets if |X
2| < k
2 for any k-element subset X of G. For each group G, there is a unique m = m
G
such that G has the small square property on (m + 1)-sets but not on m-sets. In this paper we show that given any positive integer d, there is a finite group G with m
G
= d. 相似文献
6.
《代数通讯》2013,41(9):4215-4243
Abstract A Hughes cover for exponent p(pa prime number) of a finite group is a union of subgroups whose (non-empty) complement consists of elements of order p. A proper Hughes subgroup is an instance of a Hughes cover; and its parent group is soluble by a well-known result of Hughes and Thompson. More generally an earlier result of the authors shows that a group with a Hughes cover of fewer than psubgroups is soluble. This article treats the insoluble groups having a Hughes cover for exponent pwith exactly psubgroups: the almost simple groups with this property form a restricted class of projective special linear groups. 相似文献
7.
Let F q be a finite field of characteristic two, S be a nonsingular non-alternate symmetric matrix over F q and Ps n (F q , S) be the associated pseudo-symplectic group. Let Ps n (F q , S) act linearly on the polynomial ring F q [x 1,…, x n ]. In this note, we find an explicit set of generators of the ring of invariants of Ps n (F q , S) for n = 2, 4 and 2ν +1. In particular, the results assert that the ring of invariants of Ps 4(F q , S) is not a polynomial algebra but is an example of hypersurface and the ring of invariants of Ps 2ν+1(F q , S) is a complete intersection. 相似文献
8.
51. IntroductionIt is quite clear that the ekistence of complements for some families of subgroups of agroup gives a lot ofinfor~ion about its structure. FOr instance, Hall[6] proved that a groupG is supersoluble with elementary abelian Sylow subgroups if and only if G is complemellted,that is, every subgroup of G is comPlemeded in G. The same anchor also proved that agroup is soluble if and only if every Sylow subgroup is complemellted (see [3;I,3.5]). Morerecelltly, Arad and Wardll] pro… 相似文献
9.
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
10.
11.
12.
给出了满足下列性质P_4的有限群的分类,对任意4个不同的非中心的共轭类,它们的代表元的阶的公因子为1. 相似文献
13.
有限群G的子群H称为G的c-可补子群(c-正规子群),如果存在G的子群(正规子群)N, 使得 G = NH 且 N\cap H \leq H_G,这里 H_G =\bigcap\limits_g\in G H^g 是 H 在 G 中的核.每个子群都c-可补(c-正规)的有限群称为有限c-可补群(CN-群).本文研究有限CN-群与有限c-可补群, 获得了CN- 群与c-可补群的一些新的结果.特别地, 在方法上有一定的创新, 完善近期关于CN-群的研究. 相似文献
14.
Jiangtao Shi 《代数通讯》2013,41(9):3346-3355
The aim of this article is to give a new characterization of the solvability of finite groups by some quantitative properties of their non-nilpotent proper subgroups. 相似文献
15.
16.
A. I. Budkin 《Algebra and Logic》2005,44(4):213-218
Let qG be a quasivariety generated by a group G and
be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose
is contained in a quasivariety generated by the following two groups: a free 2-nilpotent group F2(
2) of rank 2 and a free metabelian (i.e., with an Abelian commutant) group F2(
2) of rank 2. It is proved that either
= qF2(
2) or
= qF2(
2) in this instance.__________Translated from Algebra i Logika, Vol. 44, No. 4, pp. 389–398, July–August, 2005. 相似文献
17.
18.
Guohua Qian 《代数通讯》2013,41(12):5183-5194
Let G be a finite group and M n (G) be the set of n-maximal subgroups of G, where n is an arbitrary given positive integer. Suppose that M n (G) contains a nonidentity member and all members in M n (G) are S-permutable in G. Then any of of the following conditions guarantees the supersolvability of G: (1) M n (G) contains a nonidentity member whose order is not a prime; (2) all nonidentity members in M n (G) are of prime order, and all cyclic members in M n?1(G) of order 4 are S-permutable in G. 相似文献
19.
A group G is metahamiltonian if all its non-abelian subgroups are normal. It is proved here that a finitely generated soluble group is metahamiltonian if and only if all its finite homomorphic images are metahamiltonian; the behaviour of soluble minimax groups with metahamiltonian finite homomorphic images is also investigated. Moreover, groups satisfying the minimal condition on non-metahamiltonian subgroups are described. 相似文献
20.
《代数通讯》2013,41(5):1289-1302
ABSTRACT Let x be a p-element of a finite group G. We say that x is unfused in G if, for some Sylow p-subgroup S of G containing x, all G-conjugates of x in S are S-conjugates. It is shown (using the classification of finite simple groups) that a finite group that contains an unfused involution has a chief factor of order 2. 相似文献