A Classification of Metacyclic 2-Groups
A Classification of Metacyclic 2-Groups
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DOI：
10.1142/s1005386706000058
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发表时间：
2006-03
影响因子：
0.3
通讯作者：
Mingyao Xu;Qinhai Zhang
中科院分区：
文献类型：
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作者：
Mingyao Xu;Qinhai Zhang
一个有限p-群G称为亚循环群，如果它有一个循环正规子群A使得G/A是循环的。1973年，King对亚循环p-群进行了分类; 1987年，纽曼和第一作者通过p-群生成算法提出了亚循环p-群的一种新方法，他们发现了这些群的新表示。然而，他们的结果只在p奇数的情况下公布，并没有给出证明。本文的目的是在p=2的情形下给出他们的结果的一个新的证明，它与p-群生成算法无关.
A finite p-group G is called metacyclic if it has a cyclic normal subgroup A such that G/A is cyclic. In 1973, King classified metacyclic p-groups; in 1987, Newman and the first author developed a new approach to metacyclic p-groups suggested by the p-group generation algorithm, they found new presentations for these groups. However, their results were only announced in the case of p odd, and no proof was given. The purpose of this paper is to give a new proof of their results in the case of p=2, which is independent of the p-group generation algorithm.