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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… Click to show full abstract
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.
Keywords:
element order;
order;
average element;
conjugacy classes;
order number;
number conjugacy
Journal Title: Journal of Algebra
Year Published: 2020
Link to full text (if available)
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Journal Title: Journal of Algebra
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!