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1.
《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   

2.
《代数通讯》2013,41(5):2019-2027
Abstract

A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this paper we examine the structure of a finite group G under the assumption that certain abelian subgroups of prime power order are S-quasinormally embedded in G. Our results improve and extend recent results of Ramadan [Ramadan, M. (2001). The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups. Arch. Math. 77:143–148].  相似文献   

3.
Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively.  相似文献   

4.
Abstract

A subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded.  相似文献   

5.
Abstract

A subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded.  相似文献   

6.
《代数通讯》2013,41(5):1895-1902
Abstract

Let R be a local ring, with maximal ideal m , and residue class division ring R/ m ?=?D. Denote by R*?=?G L 1(R), the group of units of R. Here we investigate some algebraic structure of subnormal and maximal subgroups of R*. For instance, when D is of finite dimension over its center, it is shown that finitely generated subnormal subgroups of R* are central. It is also proved that maximal subgroups of R* are not finitely generated. Furthermore, assume that P is a nonabelian maximal subgroup of R* such that P contains a noncentral soluble normal subgroup of finite index, it is shown that D is a crossed product division algebra.  相似文献   

7.
Baer and Wielandt in 1934 and 1958, respectively, considered that the intersection of the normalizers of all subgroups of G and the intersection of the normalizers of all subnormal subgroups of G. In this article, for a finite group G, we define the subgroup S(G) to be intersection of the normalizers of all non-cyclic subgroups of G. Groups whose noncyclic subgroups are normal are studied in this article, as well as groups in which all noncyclic subgroups are normalized by all minimal subgroups. In particular, we extend the results of Passman, Bozikov, and Janko to non-nilpotent finite groups.  相似文献   

8.
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 HK ≤ 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   

9.
Let G be a reductive real Lie group, an involutive automorphism of G, and L=G the fixed point set of . It is shown that G has only finitely many L-conjugacy classes of parabolic subgroups, so if P is a parabolic subgroup of G then there are only finitely many L-orbits on the real flag manifold G/P. This is done by showing that G has only finitely many L-conjugacy classes of -stable Cartan subgroups. These results extend known facts for the case where G is a complex group and L is a real form of G.Research partially supported by NSF Grant GP-16651.  相似文献   

10.
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 TH ≤ 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   

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