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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Acknowledgment
The authors are grateful to the referee for many helpful suggestions and for shortening the proofs of Lemma 2.7 and Theorem 1.3.
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The first author was supported by the DFG grant MO 3377/1-2.
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Morotti, L., Tong-Viet, H.P. Proportions of vanishing elements in finite groups. Isr. J. Math. 246, 441–457 (2021). https://doi.org/10.1007/s11856-021-2256-4
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DOI: https://doi.org/10.1007/s11856-021-2256-4