论文标题
有限的$ p $ - 组的循环亚组数量的第二个最小值/最大值
The second minimum/maximum value of the number of cyclic subgroups of finite $p$-groups
论文作者
论文摘要
令$ c（g）$为有限组$ g $的环状亚组的poset，让$ \ m natercal {p} $是$ p $ - 订单$ p^n $的类别（$ n \ geq 3 $）。考虑功能$α：\ Mathcal {p} \ longrightArrow（0，1] $由$α（g）= \ frac {| c（g）|} {| g |} $。在本文中，我们确定$α$的第二个最小值的最低值，以及第二$ $ n $ po = wes $ n $ n $ a $ nimimim y n $ a $。奇数的情况和我们概述了这方面的结果。
Let $C(G)$ be the poset of cyclic subgroups of a finite group $G$ and let $\mathcal{P}$ be the class of $p$-groups of order $p^n$ ($n\geq 3$). Consider the function $α:\mathcal{P}\longrightarrow (0, 1]$ given by $α(G)=\frac{|C(G)|}{|G|}$. In this paper, we determine the second minimum value of $α$, as well as the corresponding minimum points. Further, since the problem of finding the second maximum value of $α$ was completely solved for $p=2$, we focus on the case of odd primes and we outline a result in this regard.
