循环群是—种很重要的群,也是已被完全解决了的—类群。其定义为若—个群G的每—个元都是G的某—个固定元a的乘方,则称G为循环群,记作G=(a),a称为G的—个生成元。循环群有无阶循环群和有阶循环群两种类型。
We prove: In a non-cyclic group, if the number of non-power subgroups is finite, then the group is finite.
证明了如果非循环群的非幂子群个数有限,那么它就是有限群。
参考来源 - 群的共轭性质与可分性质Prime group must be cyclic group. So it is widely used in Cryptography.
素数阶群必是循环群且除单位元之外皆为生成元,故在基于离散对数的密码系统中有重要的应用。
参考来源 - 素域F·2,447,543篇论文数据,部分数据来源于NoteExpress
而对于亚循环群的DCI -性,目前所知的结果并不多。
But for the problem of the DCI-property of metacyclic groups, there are still not many results.
具体地构造出两个有限循环群的自由积的外自同构群,并给出了其阶的计算公式。
The outer automorphism group of the free product of two cyclic groups is constructed, and two exact formulas for calculating its order are established.
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