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arXiv · 2007.16081

Proportions of vanishing elements in finite groups

Lucia Morotti·Hung P. Tong-Viet
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Abstract

In this paper, we study the proportion of vanishing elements of finite groups. We show that the proportion of vanishing elements of every finite non-abelian group is bounded below by $1/2$ and classify all finite groups whose proportions of vanishing elements attain this bound. For symmetric groups of degree at least $5$, we show that this bound is at least $2327/2520$ which is best possible.

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Lucia Morotti, Hung P. Tong-Viet. 2020-07-31. Proportions of vanishing elements in finite groups. https://arxiv.org/abs/2007.16081

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