Some Necessary and Sufficient Conditions of Abelian Groups and Cyclic Groups
Some Necessary and Sufficient Conditions of Abelian Groups and Cyclic Groups
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发表时间：
2006
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通讯作者：
HE Xuan-li
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作者：
HE Xuan-li
Abel子群的中心化子与正规化子在有限群的结构中起着重要的作用.本文考虑了一些Abel子群，如二元生成的Abel子群、初等Abel子群、极大Abel子群、循环子群、极小Abel子群，它们的中心化子与正规化子相等，从而得到了Abel群与循环群的一些充要条件，并改进了文献[2]中的Zassenhaus定理和陈仲木定理0.3。
The centralizers and normalizers of abelian subgroups play a strong part in the structure of finite groups.In this paper,we consider some abelian subgroups,such as abelian subgroups generated by two elements,elementary abelian subgroups,maximal abelian subgroups,cyclical subgroups,minmal subgroups,whose centralizers are equal to its normalizers,so we obtain some necessary and sufficient conditions of abelian groups and cyclic groups,and improve Zassenhaus Theorem and Chen Zhongmu,Theorem 0.3 in Reference [2].