Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the twisted Alexander vanishing order of a knot to be the minimal order of the finite groups such that the corresponding twisted Alexander polynomial is zero. In this paper, we show its basic properties, and provide several explicit values for knots with 10 or fewer crossings. Moreover, we characterize a finite group admitting the twisted Alexander polynomial to be zero.
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Ishikawa et al. (2026) studied this question.
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