论文标题
本地循环基团的产品
Products of locally cyclic groups
论文作者
论文摘要
我们考虑$ g = ab $的组，其中有两个本地循环子组$ a $和$ b $。这些组的结构是在$ a $ a和$ b $的情况下确定的，或者当一个是周期性的，而另一个则不是。加上先前对$ a $ a $ b $无扭力的案件的研究，这使所有属于两个本地循环群体的乘积提供了完整的分类。还表明，有限数量的成对透明周期性周期性循环亚组的乘积是局部超溶群。
We consider groups of the form $G=AB$ with two locally cyclic subgroups $A$ and $B$. The structure of these groups is determined in the cases when $A$ and $B$ are both periodic or when one of them is periodic and the other is not. Together with a previous study of the case when $A$ and $B$ are torsion-free, this gives a complete classification of all groups that are the product of two locally cyclic groups. It is also shown that the product of a finite number of pairwise permutable periodic locally cyclic subgroups is a locally supersoluble group.
