论文标题
有限组的平均元素顺序和共轭类别的数量
The average element order and the number of conjugacy classes of finite groups
论文作者
论文摘要
令$ o（g）$为$ g $元素的平均订单，其中$ g $是有限组。我们表明，即使$ n \ trianglelefteq g $，也没有$ o（g）$的多项式下限，即使$ g $是Prime-Power订单组，而$ n $也是Abelian。这给了A. Jaikin-Zapirain的问题负面答案。
Let $o(G)$ be the average order of the elements of $G$, where $G$ is a finite group. We show that there is no polynomial lower bound for $o(G)$ in terms of $o(N)$, where $N\trianglelefteq G$, even when $G$ is a prime-power order group and $N$ is abelian. This gives a negative answer to a question of A.~Jaikin-Zapirain.
