Abstract
Abstract Let 𝐺 be a finite group and let P v ( G ) \mathrm{P}_{\mathbf{v}}(G) be the proportion of elements g ∈ G g\in G such that χ ( g ) = 0 \chi(g)=0 for some irreducible character 𝜒. In a recent paper, we proved that if P v ( G ) < P v ( A 7 ) \mathrm{P}_{\mathbf{v}}(G)<\mathrm{P}_{\mathbf{v}}(A_{7}) , then P v ( G ) = ( m − 1 ) / m \mathrm{P}_{\mathbf{v}}(G)=(m-1)/m for some 1 ≤ m ≤ 6 1\leq m\leq 6 . Here we classify all the finite groups 𝐺 such that P v ( G ) = ( m − 1 ) / m \mathrm{P}_{\mathbf{v}}(G)=(m-1)/m and m = 1 , 2 , … , 6 m=1,2,\ldots,6 .
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