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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
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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
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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
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李志秀 《数学的实践与认识》2016,(14):294-296
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
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《中国科学 数学(英文版)》2010,(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
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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
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《中国科学 数学(英文版)》2020,(7)
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
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Haipeng Qu 《Israel Journal of Mathematics》2013,195(2):773-781
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
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ZHANG JunQiang & LI XianHua School of Mathematical Sciences Soochow University Suzhou China 《中国科学 数学(英文版)》2010,(5)
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
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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
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Zvonimir Janko 《Archiv der Mathematik》2011,96(2):105-107
We give here a complete classification of the title groups (Theorem A). 相似文献
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EPULIC Vladimir 《中国科学A辑(英文版)》2009,52(2):254-260
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