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1.
非极大交换子群皆正规的有限群   总被引:1,自引:0,他引:1  
设H是有限群G的一个交换子群.如果H在G中的中心化子正是它本身,则称H为G的极大交换子群.本文主要研究每一非极大交换子群都正规的有限群的结构,对这类有限群给出其完全分类.  相似文献
2.
ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS   总被引:1,自引:0,他引: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
3.
二次极大子群皆是$PSC^{*}$-群的有限群   总被引:1,自引:0,他引:1       下载免费PDF全文
This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC^*-groups.  相似文献
4.
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
5.
关于有限群的S-半置换子群   总被引:1,自引:0,他引:1       下载免费PDF全文
Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under the assumption that every member in Md(Gp) is S-semipermutable in G for each prime divisor p of |G| and a Sylow p-subgroup Gp of G.  相似文献
6.
In this note, we prove that if G is a finite group, then G is p-nilpotent if and only if there exists a positive integer n such that for any x,y∈G.  相似文献
7.
In this note, we prove that if G is a finite group, then G is p-nilpotent if and only if there exists a positive integer n such that for any x,y∈G.  相似文献
8.
For a prime divisor of the order of a finite group , we present the set of -subgroups generating . In particular, we present the set of primary subgroups of generating the last member of the lower central series of . The proof is based on the Frobenius Normal -Complement Theorem and basic properties of minimal nonnilpotent groups. Let be a group and a group-theoretic property inherited by subgroups and epimorphic images such that all minimal non--subgroups (-subgroups) of are not nilpotent. Then (see the lemma), if is generated by all -subgroups of it follows that is a -group.

  相似文献

9.
本文给出了有限交换局部环R上无限线性群GL(R)=∪nGLnR的Sylowp-子群的形式.令M是有限交换局部环R的唯一极大理想,k=R/M为R的剩余类域.用X(k)表示k的特征,并假定P与x(k)互素.作者证明了:GL(R)的任一Sylowp-子群S或者同构于的可数无限直积与P(j)的无限直积的直积(当P≠2或P=2,X(k)β≡1(mod4))或者同构于Pi的无限直积与P(j)的无限直积的直积(当P=2,X(k)β≡3(mod4)),这里,只是GL(epi)R(分别地,GL(2ri)R)的Sylowp-子群,P(j))同构于P=∪i∈Ipi,I是可数集.  相似文献
10.
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 HK ⩽ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S 4-free and every minimal subgroup of PG N is c-supplemented in N G (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
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