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1.
本文利用子群计数刻画了型不变量为(p~k,p,p,…,p)的交换p群以及亚循环的内交换p群(其中p为奇素数).  相似文献   

2.
该文分类了任意两个非交换元均生成 p3阶子群的有限 p -群.作为推论, 完全解决了文献[1]中提出的第237个问题: 对于所有的 x,y∈ G, 研究满足条件( x, y) |≤p3的 p -群 G.  相似文献   

3.
完全分类了满足|I_3(G)|=4的有限2群,其中I_k(G)表示G的所有p~k阶子群的交.  相似文献   

4.
内交换p-群的中心扩张(I)   总被引:2,自引:1,他引:1  
设N,H为群. H被N的中心扩张是关于群的短正合序列:满足N≤Z(G).本文完全分类了当|N|=p,H为内交换p-群时, H被N的中心扩张所得的群.    相似文献   

5.
张军强  黎先华 《中国科学A辑》2009,39(12):1403-1408
设G是一个有限p-群.若G的真子群的导群的阶都整除pi,则称G为Di-群.我们给出了所有D1-群的一个刻画.这回答了Berkovich提出的一个问题.  相似文献   

6.
研究了内交换p-群G是capable群需要满足的条件,得到了这类群是capable群的充要条件.并由内交换p-群G构造得到了群H,使得H满足HH/Z(H)≌G.  相似文献   

7.
Blackburn, Deaconescu和 Mann 的文章[1], 群G叫做平衡群,如果对G的满足HK=KH的任意子群H,K, 或者H 属于K的正规化子,或者K 属于H的正规化子.继续Blackburn, Deaconescu和 Mann 的工作,并基于 Newman和本文第四作者关于亚循环p-群的分类(见文[4,5],也见文[8]),我们在本文中给出了有限二元生成平衡p-群的完全分类。  相似文献   

8.
徐勇  冯爱芬  孙炎冰 《数学杂志》2015,35(3):743-746
本文研究了子群交换度与有限群结构的关系.利用子群交换度的数量性质,获得了循环群和2n阶的广义四元数群的一个新刻画.  相似文献   

9.
10.
有限对称群的子群   总被引:1,自引:0,他引:1  
  相似文献   

11.
A subgroup A of a p-group G is said to be soft in G if CG(A) = A and |NG(A)/A| = p. In this paper we determined finite p-groups all of whose maximal abelian subgroups are soft; see Theorem A and Proposition 2.4.  相似文献   

12.
In this paper, we classify the finite p-groups all of whose non-abelian proper subgroups are metacyclic and answer a question posed by Berkovich. Received: 22 June 2005  相似文献   

13.
For an odd prime p, we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic, and based on the criterion, the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism. This solves a problem proposed by Berkovich.  相似文献   

14.
Assume G is a direct product of M p (1, 1, 1) and an elementary abelian p-group, where M p (1, 1, 1) = 〈a, b | a p = b p = c p =1, [a,b]=c,[c,a] = [c,b]=1〉. When p is odd, we prove that G is the group whose number of subgroups is maximal except for elementary abelian p-groups. Moreover, the counting formula for the groups is given.  相似文献   

15.
Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich.  相似文献   

16.
In this paper, we classify the finite p-groups all of whose non-abelian proper subgroups are generated by two elements.  相似文献   

17.
18.
19.
We give here a complete classification of the title groups (Theorem A).  相似文献   

20.
On finite 2-groups all of whose subgroups are mutually isomorphic   总被引:1,自引:0,他引:1  
In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabelian maximal subgroups. After that, we investigate the structure of isomaximal groups of order less than 64. Finally, in Theorem 14. we show that the minimal nonmetacyclic group of order 32 possesses a unique isomaximal extension of order 64. This work was supported by Ministry of Science, Education and Sports of Republic of Croatia (Grant No. 036-0000000-3223)  相似文献   

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