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On the proportion of vanishing elements in finite groups

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arxiv 2201.00550 v3 pith:CQ6Q2V22 submitted 2022-01-03 math.GR

On the proportion of vanishing elements in finite groups

classification math.GR
keywords elementsfinitemathrmproportioncharactersfunctiongroupgroups
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We prove that the function $\mathrm{P}_{\mathrm{v}}(G)$, measuring the proportion of the elements of a finite group $G$ that are zeros of irreducible characters of $G$, takes very sparse values in a large segment of the $[0,1]$ interval.

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