Finite p-groups whose non-normal cyclic subgroups have small index in their normalizers

被引：14
|
作者：
Zhang, Xiaohong [1 ]
Guo, Xiuyun [2 ]
机构：
[1] Ningbo Univ Technol, Coll Sci, Ningbo 315211, Zhejiang, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
JOURNAL OF GROUP THEORY | 2012年 / 15卷 / 05期
基金：
中国国家自然科学基金;
关键词：
D O I：
10.1515/jgt-2012-0009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A p-group is called an N(p)m group if all of its non-normal cyclic subgroups have index no more than p(m) in their normalizers. In this paper we prove that the order of a non-Dedekind N(p)m group cannot exceed p((2m+1)(m+1)) when p > 2. We also completely classify non-Dedekind N(p)2 groups for p > 2.
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页码：641 / 659
页数：19
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