论文标题
具有12个环状亚组的组
Groups having 12 cyclic subgroups
论文作者
论文摘要
如果有限组包含$ n $ cyclic子组，则有限组为$ n $ cyclic。对于有限的$ g $，环状亚组与子组数量的比率称为$ g $的循环度，并由$ cdeg（g）$表示。在本文中，我们对所有$ 12 $ - 环保组进行了分类。我们还证明，所有有限组的循环度均在$ [0,1] $中密集，它可以解决[20] In [20]中的tinmentrnăuceanu和tóth所要求的问题，“对于[0，1] $，都存在一个$ \ lim_ fim_ fim_n \ in [0，1] $，for In [0，1] $。 cdeg（g_n）= a $“？
A finite group is said to be $n$-cyclic if it contains $n$ cyclic subgroups. For a finite group $G$, the ratio of the number of cyclic subgroups to the number of subgroups is known as the cyclicity degree of the group $G$ and is denoted by $cdeg (G)$. In this paper, we classify all $12$-cyclic groups. We also prove that the set of cyclicity degrees for all the finite groups is dense in $[0,1]$, which gives a solution to the problem asked by Tărnăuceanu and Tóth in [20] "For every $a\in [0, 1]$, does there exist a sequence $(G_n)$ of finite groups such that $\lim_{n\to\infty} cdeg(G_n)=a$ "?
