论文标题
有限组的循环亚组数量的结果
A result on the number of cyclic subgroups of a finite group
论文作者
论文摘要
令$ g $为有限的组，$α（g）= \ frac {| c（g）|} {| g |} $ \ ,, $ c（g）$表示$ g $的循环子组集。在此简短说明中，我们证明$α（g）\leqα（z（g））$，我们描述了相等性发生的$ g $。这为有限的团体提供了一些足够的条件，即$ 4 $ -ABELIAN或ABELIAN。
Let $G$ be a finite group and $α(G)=\frac{|C(G)|}{|G|}$\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $α(G)\leqα(Z(G))$ and we describe the groups $G$ for which the equality occurs. This gives some sufficient conditions for a finite group to be $4$-abelian or abelian.
